A TREATISE ON MILLING 
AND MILLING MACHINES 



► -....-.--• 



The Cincinnati Milling Machine Co. 
CINCINNATI, OHIO, U. S 





Class T"P i 2. P.*? 

COPYRIGHT DEPOSIT. 



A TREATISE ON 

MILLING 



AND 



MILLING MACHINES 



Price, $1.50 



FOURTEENTH THOUSAND 



COPYRIGHT, 1922, BY 

THE CINCINNATI MILLING MACHINE 

COMPANY 

CINCINNATI, OHIO 



T3 \ZjZj%~ 

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THE PLANT IN WHICH 
CINCINNATI MILLERS ARE MADE 



This company commenced making Milling Machines 38 years 
ago. From a small beginning in rented quarters the business has 
grown to the proportions indicated by the size of the present plant. 

This illustration is made from a scale drawing and shows the 
plant as it actually is today. The machine shop building is 810 
feet long; combined length of all the buildings 1450 feet. The 
three-story front is 380 feet wide. The entire plant, exclusive of 
the power plant, has 10}^ acres (455,000 square feet) of floor space. 
It is the largest plant in the world devoted exclusively to the manu- 
facture of Milling Machines and Grinders. 

Visitors are cordially welcome to inspect this plant at all 
times. 

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PREFACE 



The past few years have seen an unusually rapid development 
in the art of milling. We have carried out some very exhaustive 
experiments in cutter design, cutter and work cooling, and other 
branches of the art, which have led to marked improvements, not 
only in these particular branches, but in the Milling Machine itself. 

Although some of the data pertaining to these developments 
have already appeared in various publications, we believe that their 
compilation in complete form, as found in this book will make 
them of much more general use to those interested in, and responsi- 
ble for, efficient production from Milling Machines. A more com- 
plete knowledge of the action of milling cutters, the effect that 
action has on production, a familiarity with the different construc- 
tions and types of milling fixtures and holding devices, the cause of 
unsatisfactory Milling Machine performance and the basic prin- 
ciples of cutter sharpening, are all necessary for the intelligent 
application of the modern Milling Machine. 

We have in this book given considerable space to various phases 
of these subjects, and to this end are presenting some matter never 
before published. 

The mathematical chapters dealing with the computations 
involved in cutting spur, bevel, spiral and worm gears, present 
these subjects in a simple, detailed manner, which will, we believe, 
make them clear and useful to those for whom the usual method 
of presentation of this matter has always been too much involved. 

The arrangement of the various formulas and mathematical 
tables will prove of convenience to all who have occasion to use them. 

The formulas and diagrams in the chapters on gearing have 
been adapted from Machinery's Handbook and are printed by 
permission of the publishers. 



The Cincinnati Milling Machine Company 



CONTENTS 

CHAPTER I page 

The Construction and Use of Milling Machines 7 

CHAPTER II 

Erection, Care and Adjustment of Milling Machines 74 

CHAPTER III 

Toolroom Millers— The Dividing Head, etc 86 

CHAPTER IV 

Setting up the Machine 108 

CHAPTER V 

An Analysis of the Process of Milling 122 

CHAPTER VI 

Milling Machine Feeds 132 

CHAPTER VII 

Speeds of Milling Cutters 135 

CHAPTER VIII 

Stream Lubrication — Cutter and Work-Cooling System . . . 156 

CHAPTER IX 

Milling Cutters — Notes on the Design and Efficiency of 
Modern Cutters 171 

CHAPTER X 

Cutter Sharpening 203 



A Treatise on Milling and Milling Machines 5 

CHAPTER XI page 

Power Required to do Milling 213 

CHAPTER XII 

Various Methods of Milling 217 

CHAPTER XIII 

Milling Jigs and Fixtures 229 

CHAPTER XIV 

The Sizing and Cutting of Spur Gears 279 

CHAPTER XV 

Shop Trigonometry — Bevel Gears and their Calculation — 
Instructions for Cutting 299 

CHAPTER XVI 

Spiral Gear Cutting — Calculations, Formulas, Tables, etc. 323 

CHAPTER XVII 

Worm Gearing — Calculations and Methods of Cutting .... 342 

CHAPTER XVIII 

Continued Fractions and their Application to Shop Prob- 
lems — Angular Indexing 351 

CHAPTER XIX 

Change Gears for Cutting Spirals 364 

CHAPTER XX 

Cams — Tables for Setting the Milling Machine for Milling 
Spiral Cams 377 

CHAPTER XXI 

Tables of Natural Trigonometric Functions 417 



The Cincinnati Milling Machine Company 




M-Type Universal Cincinnati Miller 

With Constant Speed Drive 

Made in the No. 1 and No. 2 Sizes 
(Patent Rights Fully Reserved) 



A Treatise on Milling and Milling Machines 



CHAPTER I 

THE CONSTRUCTION AND USE OF 
MILLING MACHINES 

Before entering into an analysis of the process of milling, the 
design of milling cutters, jigs, fixtures, etc., and the mathematics 
involved in the setting up of the machine for some classes of milling, 
it may be best to first examine into the construction of the machines 
and attachments available. 

Classification of Machines. In this book we will confine our- 
selves to the Column and Knee Type Milling Machines and the 
smaller sizes of Manufacturing Millers in most general use. These 
comprise the types of machines with which everyone is more or less 
familiar. They are the machines that are used in the toolroom, 
in the jobbing shop, for model work, repair shops and for manu- 
facturing. 

Universal Milling Machines, so called because of the great range 
of work that they will accommodate, are arranged with a swiveling 
table, and regularly equipped with a dividing head. They can thus 
be used, in addition to a general line of milling, for all sorts of indexing 
and milling work between centers, such as spur and spiral gears, 
and also on angular work, such as bevel and mitre gears. Each 
toolroom should contain one or more of these Universal Machines. 

Plain Milling Machines are similar to the Universals, differing 
only in that the Plain Machines do not have a swiveling table, and 
that their equipment does not include index centers of any sort. 
They are used both in the toolroom and for regular manufacturing. 

Vertical Milling Machines are similar to the Plain Milling 
Machines, with this exception — that the spindle is in a vertical 
position, and at right angles to the plane of the table. They are 
particularly adapted for the use of face and end mills in the manu- 
facturing department, for the milling and boring of jigs in the 
toolroom, and for the machining of dies. 

Manufacturing Millers are particularly adapted for repetition 
work produced in large quantities. They are, generally speaking, 



8 The Cincinnati Milling Machine Company 

simpler in construction than the Knee Type Millers, and are used in 
large quantities in the manufacture of firearms, typewriters, auto- 
mobiles, etc. All of these machines will be briefly described in the 
following pages. 

The Selection of a Milling Machine. The selection of the 
type of Miller best adapted for the economical production of a given 
class of work can not be given too careful consideration. The quan- 
tity and quality of work that the machine will produce must 
justify the investment. 

We have gone far towards helping our customers in the solution 
of their milling problems and have thus gained a wider knowledge 
of the economic field of milling than can be obtained from the limited 
experience of one shop on one class of work. 

We are prepared to make complete time studies of all the milling 
operations on any piece of work, suggest methods, fixtures, etc., 
and furnish the complete equipment for doing it. 

Our wide experience in this work and the great variety of milling 
machines made by us, enable us to recommend and furnish that size, 
style and type of machine which will prove most economical in view 
of all the conditions attendant upon its installation and use. 

It would hardly be appropriate to attempt to deal here with all 
the considerations upon which an intelligent selection of a machine 
depends, but mention of the most important factors will, we believe, 
prove helpful. 

Whether it should be a Cone-Driven or a Constant Speed Drive 
type machine depends on — 

The quantities in which parts are made. 

The kind of work to be milled. 

Power required. 

Method of transmission used, whether by line shaft, group 
drive or individual motor drive. 

Whether it should be Plain, Universal or Vertical depends on — 

Whether it will be one of many machines or the only Milling 
Machine in the department. 

The amount of time it will be used for spiral cutting. 

Whether it will be used for jobbing or manufacturing. 



A Treatise on Milling and Milling Machines 9 

Whether for machining flat surfaces, die sinking or gang 
work. 

Whether it should be an Automatic depends on the quan- 
tities in which the parts are made. 

The suggestions contained in the illustrations of machines in 
operation will be helpful in the selection of the proper machine. 

Plain Milling Machines. These are made in both the Con- 
stant Speed Drive type and the Cone-Driven type. The rapid 
development of the use of Milling Machines is constantly extend- 
ing their field into heavier work, demanding more power at the 
cutter and therefore, increased strength and rigidity in the machines. 
This development has led to the design of the constant speed drive 
machines. In their design the spindle power is not handicapped by 
the limitations of a driving cone, and for all practical purposes it 
may be assumed that the constant speed belt drive delivers the 
same power to the cutter at all spindle speeds, so that the operator 
knows just what can be expected from the machine under all 
conditions. 

These machines lend themselves to Direct Connected Motor 
Driving. They may be driven direct from the line shaft. A coun- 
tershaft is not necessary. We make them in three different designs, 
each especially developed for the sort of work it is usually called 
upon to do. They are: 

The M-type, which is made in the No. 1 and No. 2 sizes. 
These are machines of medium power rating for work 
that does not call for unusual cutting capacity. 

The High Power Machines in the No. 2 and No. 3 sizes. 
These are heavy duty machines. 

Finally, the No. 4 and No. 5 High Power Machines, which 
represent the highest development in Knee Type Millers. 
Each of them is briefly described in the following pages. 



10 The Cincinnati Milling Machine Company 



MACHINE STARTING LEVER 



ADJUSTABLE BELT 
GUARD 



CHANGE GEARS FOR 
THE DIFFERENT 

FEED SERIES 



DRAIN FOR RESERVOIR FOR 
OILING INSIDE PARTS 
OF COLUMN 



OIL PUMP FURNISHED 
ON SPECIAL ORDER 




CINCINNATI STANDARD 
FLANGED SPINDLE ENC 



SERIAL NUMBER 
OF MACHINE 



.COVER FOR CLUTCH 

ADJUSTMENT 



TABLE FEED LEVER 



NARROW GUIDE FOR 
DDLE BEARINGS 



SADDLE CLAMP 
SCREWS 



CROSS FEED LEVER 



VERTICAL FEED LEVER 



FEED CHANGE LEVERS OPERATED 
FROM FRONT OF MACHINE 



FEED REVERSE LEVER 



CUTTING OIL DRAINS 
TO TANK IN BASE 



Fig. 1. Functional Diagram of the M-Type Millers Showing Some 
Important Features and Location of Operating Levers 



A Treatise on Milling and Milling Machines 



11 



CINCINNATI M-TYPE MILLERS 



These new M-type Millers embody adaptions of the mechanisms 
which proved so highly successful in other machines, such as the 
strong, wide, and solid Knee of the IS" Plain Manufacturing 
Machine, together with the principle of a sliding gear speed change 
mechanism and a feed change mechanism at the side of the knee, 
with its change levers at the front within easy reach of the operator, 
these being simplified forms of corresponding mechanisms on the 
No. 4 and No. 5 Millers. 

The Drive. The starting 
lever is within easy reach of 
the operator from his usual 
position in front of the table, 
as is evident from Fig. 2. 
The driving pul[ey is at the 
rear of the machine. It is 
enclosed by an adjustable 
belt guard, and runs 600 r. 
p. m. 

The drive is through an 
adjustable friction disc clutch 
similar in design to the disc 
clutches used on Auto- 
mobiles. The power is trans- 
mitted from the first shaft to 
to the spindle through a 
train of hardened steel gears 
and hardened shafts. 




Fig. 2 

It is easy to reach the starting lever from the 
operator's usual position. 



All of the twelve speed changes are made through selective 
sliding gears, similar to the well-known principle used in auto- 
mobile transmissions. There is no tumbler. There are never any 
gears in engagement except those providing the speed being 
used. Since the pulley runs faster than the fastest spindle 
speed, there is always a reduction in speed through the entire gear 
train. This construction greatly minimizes strains, reduces power 
losses, and increases the efficiency. 



12 



The Cincinnati Milling Machine Company 



Integral Keys. All key driven sliding members, whether 
sleeves, gears or clutches, are driven by keys cut integral with the 
shaft or the member itself. There are, therefore, no fitted keys in 
these members, which might work loose. 

Automatic Brake for Stopping Spindle. In connection 
with the driving clutch a simple brake arrangement is provided for 
automatically stopping the spindle immediately when the clutch is 
disengaged. 

The Spindle is chrome nickel steel. Its front end is fitted 
with a Cincinnati Standard Flange, which was adopted as the 
standard for all Cincinnati Millers several years ago. It has proven 
a very desirable feature because it is simple and affords complete 
interchangeability of face mills. 

We are now carrying standardization a step farther, and putting 
into these small Machines, the large No. 14 B. & S. taper hole, 
which we have adopted for our No. 4 and No. 5 Machines. This 
allows free interchangeability of Arbors. It has the further ad- 
vantage of increasing the driving strength of the Arbor. 

Adjustable Arbor Support Bearings. Unless the arbor has 
a close fitting bearing in the arbor support, chatter may result, 

and it is therefore desirable al- 
ways to keep these bearings 
closely adjusted. To accom- 
plish this, we are supplying ad- 
justable arbor bearings in the 
arbor supports, one of which is 
shown in Fig. 3. This bearing 
is tapered on the outside to fit 
the taper hole in the overarm 
bracket. There are full length 
slots on the inside and on the 
outside of the bearing. This 
construction provides adjustment by allowing the bearing to contract 
when it is drawn into the overarm bracket by means of the nut shown 
at the right. This nut is provided with a knurl which engages the 
small knurled lock nut held in place by the locking screw for locking 
the bearing in position after adjustment. Snugly adjustable support 




Fig. 3 

A sectional view of one of the adjustable 
arbor support bearings. 



A Treatise on Milling and Milling Machines 13 




Fig. 4. The Drive Box 

Showing speed change levers, and the large index plate. 

bearings contribute materially to the rigidity and accuracy, as well 
as the satisfactory operation of the machine. 

Spindle Speeds. Milling practice has constantly developed 
toward the use of faster spindle speeds, and on these new Machines 
we have provided a maximum speed of 419 revolutions while the 
slowest speed is 20 r. p. m. This slowest speed is suitable for com- 
paratively large cutters working in hard material. 

Speed Changing. All the speed changes are made by the three 
levers shown in Fig. 4. Numbers representing the different speeds 
are placed in a circular arrangement on the direct reading speed 
index plate. Each circle contains one series of speeds in sequence. 
To change the speed within any one series, that is, those contained 
in any one circle on the index, it is only necessary to turn the 
lower lever until the position of the pointer corresponds with the 
desired speed. For instance, to change from 102 r. p. m. to 183 



14 



The Cincinnati Milling Machine Company 




Fig. 5 

The operator can make most speed ch an ges 
without leaving his position in front of the machine. 



r. p. m.. the lever is moved 
to the right; in the same 
way to change from 35 r. p. 
m. to 27 r. p. m.. the lever 
is moved to the left. This 
lever may be moved in 
either direction. To change 
from one series to the other, 
the secondary le vers are 
used. For example, as 
shown in Fig. 4, to change 
from 316 r. p. m. to 27 r. p. 
m. the upper lever is moved 
from "B" to "A" and the 
lower lever from "D" to 
" C ' " . etc. The letters shown 
in connection with each 
speed on the index plate, 
correspond to the positions 
of the two secondary levers. 



The Feed is driven from the main driving shaft through bevel 
gears and a vertical shaft, which connects the spindle drive box 
and the feed box. This 
vertical shaft is square, 
and the drive from it to 
the feed box is through 
spur gears, and from 
these through mitre 
gears, which are also 

the feed reverse gears, "^ 

to the feed change 
mechanism. The verti- 
cal feed shaft is com- 
pletely enclosed by tel- 
escopic tubes. 




These Machines are 
regularly furnished with 
feeds from J o" per min- 
ute to 20" per minute. 



Fig. 6. The Feed Box 

fa at the side of the knee, and all feed changps are made 

at the front. 



A Treatise on Milling and Milling Machines 



15 



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1334 





A slower series of feeds from jV' per minute to 12" per minute, or 
a faster series from %" per minute to 30 " per minute can be furnished 
when desired. 

Feed Changing. The feed box being at the side of the knee, 
with all of the levers in front, enables the operator to make all feed 
changes from his usual 
position in front of the 
machine as shown in 
Fig. 8. The operation 
of feed changing is simi- 
lar to the operation of 
speed changing. The 
pull pins "A" and "B" 
have both IN and OUT 
positions, and the lower 
lever, which is also the 

• j i -i Fig. 7. Inside of Feed Box 

lHQeX leVd. , may De There is an automatic releasing device to protect the 

moved to either the mect -° ism from overload - 

right or the left, to change from one feed to another, in a manner 
similar to that for speed changing. In making the feed changes it 
is not necessary to follow any given sequence. 

The Table Feed 
Trip is so arranged that 
after the feed has been 
automatically tripped, 
the feed lever can be 
brought clear of the dog 
and the table feed may 
then be re-engaged, to 
feed the table in either 
direction. After the 
trip dog has passed the 
lever, a heavy spring 
pulls the lever back into 
its normal position in 
the path of the dog 
again. This feature, will 
be found valuable on a 
large number of manu- 

Feed changes are all made at the front of the machine. iacturing Operation S, 




16 The Cincinnati Milling Machine Company 

particularly on reciprocating milling jobs, or milling key ways at 
different points along the length of a shaft, and similar operations. 




Fig. 9. Left — feed disengaged. Right — method of clearing the dog to reengage feed. 

Automatic Lubrication. The upper part of the column forms 
a reservoir large enough to hold three gallons of lubricating oil. The 
outside of the main driving clutch is provided with vanes which dip 
into this oil, and running 600 r. p. m., provide ample splash lubrica- 
tion not only for the gears and shafts, but also for the bearings. 
There are large cups provided for the spindle bearings on both the 
Horizontal and Vertical Machines, from which this oil is carried 
direct to the bearings, the cups being kept full by the splash system. 

Centralized Oiling. In addition to the automatic splash sys- 
tem for the mechanism in the column, a centralized oiling system 
provides for the other mechanisms. There are large oil cups on the 
saddle, the knee and the feed box. From each of these positions a 
number of bearings are oiled. The oil cups on the saddle also oil 
the table bearings and it is not necessary to set the table to any 
special position when oiling. These oilers are at the side of the 
saddle and are never covered by the work or the fixtures. They are 
so constructed that the covers close automatically by their own 
weight. 

Cutter and Work Cooling System. The base of the Machine 
forms a six gallon tank for cutter lubricant. The lower end of the 
vertical driving shaft, which drives the feed box, extends to the 
base, and is available for driving a cutter lubricant pump. When 
desired, a centrifugal pump, having a capacity of five gallons per 
minute, can be supplied on special order. To install the pump it 
is merely necessary to raise the vertical shaft, remove the cover 
plate in which it has its lower bearing, insert the pump, and replace 
the shaft. 



A Treatise on Milling and Milling Machinks 17 




Nos. 1 M and 2 M Vertical Cincinnati Millers 
With Constant Speed Drive 



(Patent Rights Fully Reserved) 



18 



The Cincinnati Milling Machine Company 



CINCINNATI M-TYPE VERTICAL MILLERS 

In designing these machines we aimed to keep them as simple 
as is consistent with the requirements of modern milling practice. 
They are compact machines of only moderate height, so that the 
table in its tipper position is not too high above the floor for con- 
veniently handling and chucking the work, and observing the cutter 
in operation. Because of these considerations, we have decided to 
make these machines in the fixed head type only. All vertical ad- 
justments are made through the knee. With the exception of the 
upper part of the column and its mechanism, the verticals are 
identical with the Plain M-type machines of corresponding size. 



The Spindle Drive. 

Power is transmitted from 
the pulley through an ad- 
justable friction disc clutch 
to a train of hardened 
steel gears running on 
hardened shafts. The 
mechanism is similar to 
that of the Horizontal 
Machines, except that the 
back gear shaft is in a ver- 
tical position, as shown in 
Fig. 11. The back gears 
drive direct to spur gears 
keyed to the spindle, all 
of which are exact du- 
plicates of those on the 
Horizontal Machine. The 
main driving gear is there- 
fore of large diameter, suit- 
able for large face mills. This construction provides an even, smooth, 
quiet action when taking heavy cuts with large cutters. A second 




FIG. 10 
The starting lever is within easy reach from the 
operators usual position. 



A Treatise on Milling and Milling Machines 



19 



series of gears provides higher speeds for small cutters. All of these 

gears are hardened. The back gear shaft is made of high carbon 

steel and is provided with four 

integral driving keys. The back 

gear change lever is at the side 

of the column within easy reach 

of the operator. 



The Spindle. The spindle 
is chrome nickel steel. Its end 
is fitted with a Cincinnati 
Standard flange and a No. 14 
taper hole. This affords com- 
plete interchangeability of face 
mills and arbors with other 
Cincinnati Millers. 




FIG. 11. SHOWING THE SPINDLE 
DRIVE GEARING. 

All gears are hardened. The back gear 
shaft has four integral keys. 



20 



The Cincinnati Milling Machine Company 



CINCINNATI Nos. 2 and 3 HIGH POWER MILLERS 

These machines are designed for work which requires maximum 
cutting capacity. 

The main driving pulley is journaled on a bracket bolted to 
the column of the machine and is connected to the driving shaft 

by means of a disk friction clutch of large proportions. The machine 
is started and stopped through this clutch by means of a lever at 
the front of the machine. All the gears are steel and hardened. 
Those most used for speed changing are chrome nickel steel, heat 
treated and hardened, making an extremely durable drive. There 
are sixteen speeds provided. 




Fig. 12. The Complete spindle Drive 

Gears I. J, K and L are steel forgings. All others are nickel steel, heat treated, 
and'all the gears are hardened. Face gear L is the only gear keyed to the spindle. 
No gears are in mesh except those doing work. 



Fig. 12 shows the driving gears of a horizontal machine in section. 
In order to reduce torsional strains and consequent vibrations to 
a minimum, there are no gears keyed directly to shafts with the 
single exception of the main gear "L," which is keyed to the front 
end of the spindle close to the bearings. 

Another feature which gives these machines the strength and 



A Treatise on Milling and Milling Machines 21 




Fig. 13. Inside of Spindle Drive Box 

Showing driving shaft, tumbler and chain wheel for driving feed from con- 
stant speed shaft. 

rigidity which modern practice demands is the automatically 
clamped tumbler, Fig. 13 and Fig. 14. The tumbler frame is sup- 
ported from the machine frame. None of its weight comes on the 
main driving shaft. The swinging frame carrying the tumbler gear 
rocks on the trunnions "C" and is operated by means of the pilot 
wheel on the outside of the machine through 
the spiral gears "S." By means of this same 
pilot wheel the entire tumbler frame can be 
adjusted laterally. When the pilot wheel is 
turned to the right the gears are brought into 
mesh and the lug "D" of the swinging tumbler 
frame abuts on the stop pins 
governing the proper meshing. 
Now if the pilot wheel is turned 
farther to the right, the swing- 
ing frame, the tumbler frame 
and the spiral gears act as a 
system of levers and screw 
which lock the tumbler frame 
securely to its slide on the T . f Fig ' "• r Sectio t n f ro "? h T f 7 b,e ^. 

J The frame C C C is a steel casting of large dimen- 

machine frame and hold the ? i ° n 1 f • supported entirely on the dovetail bearing 

in the drive box, and the operation 01 speed changing 
SUPPOrt for the tumbler gear aS automatically clamps it to this bearing in each 
r r ° working position. 




22 



The Cincinnati Milling Machine Company 



firmly as if it were permanently bolted in place. By turning the 
pilot wheel to the left as far as it will go, the tumbler gears are 
brought out of engagement. 




Fig. 15. Outside of Speed Change Box 

All changes are made through the pilot wheel and two levers shown. 

The speeds are very easily and quickly changed by means of 
the pilot wheel above mentioned and the two levers shown in Fig. 5. 
The lever positions for each speed are clearly marked. For example : 

to obtain 115 r. p. m., the index 
plate shows corresponding to 
this number the symbols 3-BC. 
It is therefore merely neces- 
sary to move one lever to "B," 
the other to "C" and move the 
tumbler to the No. 3 position. 
By pressing lightly on the 
treadle, while moving these 
levers, the gears are given a 
sufficient amount of motion to 
facilitate easy speed changing. 
The position of the operator 

Fig. 16. Position of Operator when Changing Speeds i ■> • _ j • i ^^.^ 

He moves the lever as far as it will go and then by when changing Speeds IS shOWn 

gently pressing on the treadle the gears slowly turn 1* TTio- Ifi TVio fp>Gr\ ic HriVPTl 

and will go into position ill r Ig. J.U. 1 lie leeu Ks unvcn 




A Treatise on Milling and Milling Machines 23 




Fig. 17. The Feed Box 

This remains the same for feeds driven from spindle or 
from constant speed shaft. 

is done best while the machine is running. 



from the constant speed 
shaft and the feed plate 
reads in inches per 
minute, unless otherwise 
specified at the time the 
machine is ordered. 

The outside of the 
feed box is shown in Fig. 
17. The feed index and 
feed change levers are 
the same as for the drive 
box, but feed changing 



To Change the Feeds. Change the rate of feed by means of 
the levers and pilot wheel on feed box in the same way as the speed 
changing is done. Do this while the machine is running. You 
need therefore not use the treadle. 



STARTING LEVER 



SPEED CHANGE LEVERS 



PILOT WHEEL FOR OPERATING 
AND LOCKING 
TUMBLER. 
WHEN CHANG- 
ING SPEEDS 



HAND ADJUSTMENT FOR TABLE 

FEED CHANGE LEVERS 
AND TUMBLER LOCK. 
OPERATE WHILE RUNNING 



VERTICAL FEED TRIP DOG 



TREADLE FOR TURNING 
THE GEARS WHEN 
CHANGING 
SPEEDS 




CROMETER DEPTH GAUGE 
UICK TRAVERSE FOR HEAD 



CLUTCH FOR ENGAGING MICROMETER 
HAND ADJUSTMENT 



STOP FOR DEPTH GAUGE 
MICROMETER HAND ADJUSTMENT 



TABLE FEED OPERATING 
AND REVERSING LEVER 



CUT OUT FOR TABLE FEED GEAR TRAIN 
TABLE FEED TRIP DOGS 



QUICK RETURN 
FOR TABLE 



CROSS ADJUSTMENT 



CUT OUT FOR CROSS AND 
VERTICAL FEED GEAR TRAIN 



CROSS FEED TRIP DOGS 
VERTICAL ADJUSTMENT 



CROSS AND VERTICAL FEED OPERATING 
AND REVERSING LEVER 



Fig. 18 

Arrangement of operating levers. 



Before engaging either table, cross or vertical feed, it is always 
desirable to see that the handwheel on the end of the lead screw, 



The Cincinnati Milling Machine Company 

crass screw, or vertical adjusting screw, is disengaged from the 
clutch, as otherwise, the sudden rotation of these handwheels may 
cause injury to the operator. 

Safety Pins. Trie feed mechanism of rhese Cincinnati Millers 
is prcrii-ri ~-"~ a safety pin, which will shear when the machine 
b : verioaded with too heavy a feed before breakage occurs in any 
important part of the feed mechanism. A number of these pins 
are supplied as part of the regular equipment with the machine. 
The bushes in which these pins are located will be found just outside 
The :t'"t:-t : :~. v:. :ne ier>har_:i siie :: the i-ciee :r_ :;ir H:rr.-?:~er 
Machines. Instructions for removing the sheared and inserting 
fresh pins will be found on the envelope containing the pins, which 
accompanies the machine. 

Adjusting the Clutch of High-Power Machines. This 
friction clutch may be set so that it will slip when very delicate 
cutters are used, and can also be set up so firmly that it will transmit 
the maximum horsepower that the belt can supply. To adjust this 
clutch, remove the cover from the end of the main driving pulley, 
release the clamping screw which holds the large threaded finger 
carrier, and screw up in a right-hand direction until the proper degree 
of Diction is obtained. Tighten up the locking screw and replace 
the cover. 

The Column. Knee. Saddle and Table. A powerful spindle 
drive must be supplemented by correspondingly strong main frame 
members. In our designs we have made use of the box section 
trinripie. Tiic illustrati : ns sh:~ that trie \\::.:::::„ is 3. re:"ar.rii?/; 
box with openings only large enough for inserting the main drive 
gearing and the feed gearing. 

The base deserves especial attention. It must have sufficient 
strength to rigidly support the machine and its work, and to with- 
stand the wedging action of the cutter as discussed on page 125. 
Any tendency to spring in the manner of a diaphragm seriously 
affects the alignments as well as the rigidity of the machine. As - 
result of careful experiments, we have changed the design of our 
milling machine bases, giving them about six times the strength 
that had formerly been considered adequate. 



A Treatise on Milling and Milling Machines 



25 




High-Power Universal Cincinnati Miller 
With Constant Speed Drive 

Made in the No. 2 and No. 3 Sizes 

(Patent Rights Fully Reserved) 



26 The Cincinnati Milling Machine Company 

The Knee. Fig. 19, must cany the entire weight of the work and 
its fixture and in addition to this must resist the twisting strains 
resulting both from taking the cut and from the varying twisting 
moments set up through the changing position of the table with 
its work, in relation to the knee. 

It has been general practice to provide the knee with clamping 
levers for locking it to the column when taking a cut, but we have 
found this rapidly distorts the knee, reduces the bearing to a small 
area under the clamping screws, and ultimately it becomes impossible 
to so clamp the knee that it will not rock on the column. To avoid 
this difficulty we have eliminated knee clamps entirely, have in- 
creased very considerably the metal in the knee where it engages 
the column, and provided a long taper gib. Fig. 21. adjusted length- 




Fig. 19 

This shows the knee. Note the heavy tapered gib, which provides a full 
length metal to metal bearing at all times. 



wise, which affords at all times a full bearing on the column. This 
gib, when adjusted so as to give a nice sliding fit between these two 
members, provides a degree of rigidity that enables Cincinnati 
High-Power Millers to do heavier cutting than was previously 
possible and also to do accurate work within closer limits. 



A Treatise on Milling and Milling Machines 27 




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28 The Cincinnati Milling Machine Company 

The construction of the knee is 
clearly shown in the illustrations, 
and the line drawing indicates its 
strength at the point where it 
engages the column. 

Our tables have their bearings 
Fig - 21 at the top of the "V" along the 

The section through the knee shows its great ■ t i» j_i j i i «> j_i 

strength in the Vs. The gib always has a full OUter edge 01 the table iaCe, tUUS 
bearing at "A" through its entire length. This «• ,■> £ n .1,1 £ ,1 

gives Cincinnati High-Power Millers unusual Supporting the IUll Width 01 the 

9oMity - table. 

The Saddle is shown in Fig. 22. Its mechanism is so constructed 
that the feed is direct to the table feed screw. There are no auxiliary- 
shafts. The driving gears are close to the nut and therefore only 
a short section of the lead screw is in torsion. This contributes 
largely to the efficiency of our feeding mechanism. 

Centralized Control. A modern machine tool must be handy 
to operate. It is essential that the operator's task should be made as 
easy as possible. With this in mind we have grouped all our 
levers on that side of the machine where the operator would natur- 
ally stand when using them. The diagram, Fig. 20, shows this 
quite clearly. 

The illustration, Fig. 23, shows an added feature of handiness, 
resulting from placing a feed lever where the operator can control 
his machine from behind the table. This is indispensable when 
doing end milling, face milling, or boring on a large piece of work. 
The arrangement of the table feed levers at the front of the saddle 
enables the operator on a Vertical Machine to traverse the periphery 
of a rectangle without stopping either feed or speed. This makes 
it quite practical to mill such a piece of work without leaving an 
off -set where the cut ends. 



A Treatise on Milling and Milling Machines 



29 




' — -v&q jS 



Fig. 22. The Saddle, Lead Screw and Quick Return 

Power Quick Traverse and Return. We can equip the Nos. 
2 and 3 Plain and Vertical Machines with the Power Quick Traverse 
and Return Arrangement, Fig. 24., on special order. It is driven 




Fig. 23 

Control of feeds from behind the table, enabling the operator to see his 
cutter in engagement with the work when doing endmilling, boring, etc. 



direct from the main pulley independent of the feed mechanism and 
provides a movement forward or back at 100" per minute. The con- 
trolling lever indicates the direction and when the lever is released, 
the table stops. The feed and power quick traverse can not 
both be engaged at the same time. There are limit stops which 



30 



The Cincinnati Milling Machine Company 



prevent going beyond 
things make for safety. 
Being driven from the 
main pulley, which 
does not stop when the 
machine is shut down, 
this power quick trav- 
erse is available for 
making quick table ad- 
justments when setting 
up the machine pre- 
paratory to milling a 
piece of work. This ar- 
rangement can be fur- 
nished on our smaller 
high-power machines 
as an extra attach- 
ment. 



the limits of 



table travel. All these 







842 



Fig. 24. The Power Quick Traverse and Return 



Direct-Connected Motor Drive. We have developed a sim- 
ple and highly efficient arrange- 
ment which is shown in Fig. 25. 
The motor is mounted on a swing- 
ing base hinged to the base of the 
machine so that part of the weight 
of the motor is supported by 
the belt, keeping it at all 
times at the proper tension 
and doing away with 
the need for any atten- 
tion on the part of the 
operator. An endless 
leather belt and a 
metal belt guard are 
included in the equip- 
ment. This arrange- 
ment is suitable for 
any make or style of 
constant speed motor 

Fig. 25. The Constant Speed Belted Motor Drive Arrangement running not taster than 

Suitable for constant speed motors having a maximum 1200 r. p. m. 

speed not over 1,200 revolutions. 




A Treatise on Milling and Milling Machines 



31 




High-Power Vertical Cincinnati Miller 
With Constant Speed Drive 

As made in the No. 2 and No. 3 Sizes 
(Patent Rights Fully Reserved) 



32 



The Cincinnati Milling Machine Company 



Another style of Motor Drive Arrangement is shown in Fig. 26. 
In this case the motor is mounted on a fixed extension fastened to the 
base of the machine 
and the drive is 
through reducing 
gears and a silent 
chain to the main 
shaft of the ma- 
chine. This arrange- 
ment is suitable for 
motors of any speed 
up to 1200 r. p. m. 
The reducing gears, 
sprockets, chain, 
chain guard and base 
are all included in 
the equipment. 

Vertical Millers. 

These machines are 
similar to the High- 
Power Plain Millers in all particulars, except that the spindle is 
in a vertical position. Here again we have aimed to make a machine 




Fig. 26. The Chain Motor Drive Arrangement 

The motor is placed where it does not increase the working floor 
space of the machine. 




Fig. 27. The Spindle and Spindle Driving Gears 

These gears are made of steel and hardened. 



A Treatise on Milling and Milling Machines 33 

that will have the same degree of strength in all its important parts, 
bearing in mind that the pressure against the cutter which must be 
resisted by the members carrying the spindle is the same as the 
pressure against the piece of work on the table. 

The construction of the spindle head and its driving gearing is 
shown in Fig. 27. All the driving gears, including the mitre gears 
shown, are steel and hardened. These latter have self-contained 
bearings. The one through which the spindle passes has a long hub 
bearing which takes the entire thrust of the gears, thus relieving 
the spindle from these strains. The spindle is as long as the spindle 
in the corresponding horizontal machines. Its bearings are both 
carried in the head frame and are always a maximum distance apart. 

Vertical adjustment of the spindle is obtained by moving the 
entire head frame carrying the spindle. This frame has long bear- 
ings provided with an adjustable taper gib, and when the machine 
is in constant operation on heavy repetition work, this frame may 
be securely clamped to the body of the machine, converting it 
temporarily into a fixed head machine. 

The head adjustments are quickly made by means of a pilot- 
wheel, the head itself being counter-balanced. There is also a 
slow movement provided through worm and wormwheel when 
desired. 



34 



The Cincinnati Milling Machine Company 




Nos. 4 and 5 Universal High Power Cincinnati 

Millers 

With Constant Speed Drive 

(Patent Rights Fully Reserved) 



A Treatise on Milling and Milling Machines 



35 





1 1 1108 



Fig. 28 
Rear view of machine, showing Belt. Guard. 
The arms of the belt guard are independently ad- 
justable to suit the angle of the belt. 



CINCINNATI NO. 4 AND NO. 5 HIGH POWER 

MILLERS. 

These machines were designed to meet the need of knee type 
millers of greater capacity. 

These large machines, 
with the prevailing features 
of design, such as the V-bear- 
ings for the saddle and knee 
slides, hand operated traverse 
between cuts, cylindrical form 
of overarm, tumbler gear 
transmission, etc., are no 
longer adequate to meet these 
new requirements. With a 
full knowledge of all these 
facts before us, we made ex- 
tensive researches covering 
practically every important 
element of the milling ma- 
chine. On the completion of 
thorough tests on successful mechanisms based on these researches, 
an entirely new No. 5 Machine has been produced. It is bigger 
and stronger and handier than previous machines of the 
same rating. Because of the 
success of the No. 5 Ma- 
chines, we have embodied 
these same features in our 
new No. 4 Plain, Universal 
and Vertical Machines. Some 
of the more important fea- 
tures are described in the fol- 
lowing pages. 

The Driving Pulley is 
carried on an independent 
bracket, entirely relieving the 
main shaft of the belt pull. It 
runs on ball bearings. The 
power is transmitted from 
the main shaft to the spindle 
through a train of hardened 
steel gears, and hardened shafts. All of the sixteen speed changes 
are accomplished through Selective Sliding Gears, Fig. 29. 




Fig. 29. The Spindle Drive Gearing 

Compact self-contained unit. All gears and 
shafts are hardened. Includes spindle reverse gears. 
The bevel gear drives the feed. 



36 



The Cincinnati Milling Machine Company 




FIG. 30 

Outside of Spindle Drive Unit. Shows both speed 
change levers and pilot wheel over index plate, also 
spindle reversing lever. 



A Spindle Reversing 
Mechanism in the machine 
provides for running the spin- 
dle either right-handed or 
left-handed, by simply shift- 
ing a lever, Fig. 30. The 
spindle is chrome nickel steel. 
Its front end is fitted with 
the Cincinnati Standard 
Flange, suitable for cither 
right-hand or left-hand face 
mills and it has a No. 14 
B. & S. taper hole for large 
arbors. 



Speed Changing — All of the speed changes are made by the 
two levers and pilot wheel shown in Fig. 10. Numbers represent- 
ing the different speeds are arranged in circles on the direct 
reading speed index plate, Fig. 31. Each circle contains one series 
of speeds in sequence. To change 
the speed within any one series, it 
is only necessary to turn the pilot 
wheel until the arrow on its hub 
corresponds with the desired speed. 
For instance, to change from 16 to 20 
r. p. m. the operator turns the pilot 
wheel through one quarter of a turn, 
or from 38 to 60 r. p. m. through 
half a turn. The pilot wheel may 
be turned in either direction. For 
example, should it be desired to 
change from 228 to 443 r. p. m., 
he would naturally turn the pilot wheel to the left; to change 
from 228 to 288, he would turn to the right. The letters shown 
in connection with each speed on the index plate correspond to 
the positions of the two speed change levers on the drive box, 
Fig. 30. By these levers the change is made from one circle or 
series, to another one. For instance, should it be desired to change 
from 95 revolutions to 228 revolutions the lever at the left will 
change its position from C to D and so on. 




FIG. 31 

The direct reading speed index shows 
the lever positions for each speed. 



A Treatise on Milling and Milling Machines 



37 



The Feed 

The feed is driven from the bevel gear in the drive box, Fig. 29, 
which meshes with the bevel gear in the feed bracket, Fig. 32, located 

at the rear of the column, which 

i Wk-^^M* fe m ^ urn drives the feed box proper, 

if Kr-SflNB' i t ~ \ through a universal joint shaft. 

: ' ^ * This feed box, Figures 33 and 34, 

is at the front of the knee, on 
the right hand side, and the feed 
changes are therefore made from 
the front of the machine. 





Fig. 32 — The feed bracket on the col- 
umn connects the main drive with the 
feed change mechanism and the power 
quick traverse. Different series of feeds 
may be obtained by substituting other 
gears for the two change gears A and B. 
Only one pair of change gears is supplied 
with the machine. 



Feed Changing .—The feed 
changes are made while the machine 
is running. One single lever, shown 
in the illustration, makes all of 
these sixteen feed changes. To 
change from one feed to any other, 
the operator simply sets this lever to 
the figure representing the desired 
feed, as shown on the feed index 
plate, Fig. 35. It is not necessary 
to follow any given sequence. The 
lever may be moved up or down, or from side to side, or diagonally. 
For example, to change from %" to 30 ", the lever is moved direct 
to 30"; from 4M" direct to 
Uy 2 "; from 1" direct to 19", 
from 5^" direct to 11%", 
and so on. All that is re- 
quired is to see that the 
pointer on the lever is ad- 
jacent to the figure repre- 
senting the feed. 

Each of the separate feed 
transmission trains is con- 
trolled by an Individual 
Feed Lever, which starts, 
stops or reverses the feed. 
The direction of the lever 
shows the direction of table 
movement. Moving the lever 




Fig. 33 

Outside of feed change unit. Located'at front of 
knee. One lever makes all feed changes. The gear 
shown contains a safety coupling to protect the feed 
transmission against overload or accidents. 



38 



The Cincinnati Milling Machine Company 



to the right feeds the table to the right, moving it to the left 
feeds the table to the left, and setting it in the central position 
stops the feed. A lever at the front of the knee provides similar 




^OSINMCHES PERW*^ 



Fig. 34 

Inside of feed change unit. Contains all the gearing for 
sixteen feed changes, and the feed change mechanism. 

control for the cross feed, and another lever at the right of this 
provides similar control for the vertical feed. There is a similar 
set of individual levers at the rear of the knee for operating 
the longitudinal, cross and vertical feeds from behind the table. 
This is particularly convenient for end milling, face milling, boring 
and similar work. The rear control lever for the table feed is pro- 
vided with a locking pin by which it 
may be held in the central position, 
to lock out the table feed clutches, 
preventing any movement of the 
table. This leaves the power feed 
and the power quick traverse avail- 
able for driving the Circular Attach- 
ment, or any other attachment or 
fixture that may be driven from the 
splined shaft, provided for this 
purpose. The feeds may be auto- 
matically stopped by setting dogs in 
the usual way. All trip plungers are 
so constructed that the feed may be reversed without first moving 
the table by hand, to bring the dogs clear of the plungers. 

The Power Quick Traverse of the Table is driven independ- 
ently of the feed, direct from the main driving pulley, and therefore 




Fig. 35 

The feed index plate is at the front 
of the knee. One lever makes all the six- 
teen changes. The operator merely sets 
the lever to the figure representing the 
feed desired. 



A Treatise on Milling and Milling Machines 39 

it is always available for quickly traversing the table by power after 
the machine has been stopped. 

On Plain and Vertical Machines, the Power Quick Traverse and 
Return is controlled either by hand or automatically by dogs. 

On Universal Machines it is hand operated with the table feed 
engaged. The direction indicated by the feed lever is the direction 
of table movement. There is a Quick Traverse Lever on each side 
of the saddle. This lever has three positions. In the lower position, 
it engages the table feed. In the upper position it brings the Power 




Fig. 37 

The cross and vertical feed reverse mechanism. It also 
contains the table feed transmission shaft (center). There is 
no additional feed gearing in the knee. 

Quick Traverse into operation, and while in the central position it 
stops the table movement. When using the Power Quick Traverse, 
the lever must be held in the upper position. Releasing the lever 
automatically stops the Power Quick Traverse movement. 

Hand Control on Plain Machines is by means of the table feed 
lever at the front of the saddle, Fig. 38. It has five positions. The 
two upper positions are for power quick traverse, at 100" per minute, 
and the lower positions are for engaging and stopping the feed. 
The diagram at the top of Fig. 39, preceding Cycle A, shows the 



40 The Cincinnati Milling Machine Company 

automatic control of the table feed for milling in either direction, 
as it is used in daily milling practice. The control of the feed and 
power quick traverse is by hand by means of the table feed lever 
and the table may be automatically stopped anywhere in its travel 
by means of the dogs in the usual way. 

Intermittent Feed on Plain and Vertical Machines. — By 

simply placing one or more dogs between the two end dogs, we get 
automatic control of the table feed and power quick traverse, and the 
machine is converted into an automatic miller, with intermittent 
feed. 

It is arranged so that the same cycles of movement may be used 
when feeding in either direction. The front side of the table is 
provided with two T-slots. When feeding to the left, which is the 
normal direction on Cincinnati Millers, with the spindle running 
right-handed, the intermittent feed dogs are located in the lower 
T-slot. When feeding to the right, the dogs are reversed and placed 
in the upper T-slot. These dogs always clear the trip plunger when 
the table is traversed by hand. More than twenty different cycles 
may be gotten simply by different combinations of dogs, as illus- 
trated in the diagrams, Figures 39 and 40. 

From the above it will be seen that, to use intermittent feed with 
automatic reverse and power quick traverse, we simply add some 
dogs. If we leave these dogs off the operation of the feed of 
the machine is exactly the same as that of other millers. 




Fig. 38 

The different positions of the control lever for table feed 
and power quick traverse. 

The various feed cycles obtainable are given in detail on the 
following pages. 



A Treatise on Milling and Milling Machines 



41 




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Funcitional Diagram of the No. 4 and No. 5 High-Power Plain Millers 

Showing Important New Features of Construction and 

Operating Levers 



42 



The Cincinnati Milling Machine Company 



Some of the Feed Cvcles 



Simple Setting of Dogs for Ordinary 
Milling. Either Right or Left. Feed 
Tripped Automatically. No Different 
from Usual Practice. 



*SF 



cycle A Ordinary milling, hand controlled 
power quick return, feeding left. Feed 
to the left. stop. Quick return, stop. 



STOP 


' : . ; 












r 






CZ3 








— — 


^k 








^,-r 


"* iMf 





cycle E> Same as A, feeding right. Feed to the 
right, stop. Quick return, stop. 



— TKT- 



-S- 



3LL-?- 



cycle C Ordinary milling, automatic reverse 

and return, feeding left. Feed left , auto- 
matic reverse, quick return, stop. 



-aSLiJ — 



:ycle D Same as C, feeding right. Feed right, 
automatic reverse, quick return, stop. 



JP> 



-O- 



^3- 



CYCLE E Ordinary milling, automatic quick ap- 

proach, hand controlled power quick 
return, feeding left. Quick approach, 
feed left. stop. Quick return, stop. 



~ 3P . _ _ _ 


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BG9 






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cycle F Same as E, feeding right. Quick ap- 

proach, feed right, stop. Quick return, 
stop. 






_— 4- 



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cycle C Ordinary milling, full automatic cycle, 

feeding left. Quick approach, feed left, 
automatic reverse, quick return, stop. 



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cycle H Same as G, feeding right. Quick 

approach, feed right, automatic reverse 
quick return, stop. 



— SF 



CAST w STOP 



cycle I Quick traverse to clear cutter, feeding 

left. Quick approach, feed left, quick 
traverse, stop. Quick return, stop. 



e '<• ». =»:" 


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r=" ~* £r~ 










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cycle J Same as I, feeding right. Quick ap- 

proach, feed right, quick traverse, stop. 
Quick return, stop. 



cycle K 



Intermittent feed, hand controlled, 
power quick return, feeding left. Quick 
approach, feed left, quick traverse space, 
feed, quick traverse space, feed, etc., 
quick forward to clear, stop. Quick re- 
turn, atop. 



Fig. 39 



A Treatise on Milling and Milling Machines 



43 



Some of the Feed Cycles 



^-E$^-^& 



■(253— 






'»° 



'-r uu. 



cvcu L Same as K, feeding right. Quick ap- 
proach, feed right, quick traverse spare, 
feed, quick traverse space, feed, etc., 
quick forward to clear, stop. Quick re- 
turn, stop. 

cycle M Intermittent feed, automatic reverse 
and return, feeding left. Quick ap- 
proach, feed left, quick traverse space, 
feed, etc., automatic reverse, quick re- 
turn, stop. 




cycle N Same as M, feeding right. Quick ap- 
proach, feed right, quick traverse space, 
feed, etc., automatic reverse, quick re- 
turn, stop. 



1 — 










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CYCLE 



CYCLE P 



CYCLE Q. 



CYCLE R 



CYCLE S 



CYCLE T 



CYCLE U 



CYCLE V 



Continuous milling, one direction, full 
automatic cycle, feeding left. Quick ap- 
proach, feed left, automatic reverse, 
quick return, automatic reverse, quick 
approach, feed left, automatic reverse, 
quick return, automatic reverse, etc. 

Same as O, feeding right. Quick 
approach, feed right, automatic reverse, 
quick return, automatic reverse, quick 
approach, feed right, automatic reverse, 
quick return, automatic reverse, etc. 

Intermittent continuous milling one 
direction, full automatic cycle, feeding 
left. Quick approach, feed left, quick 
traverse space, feed left, automatic re- 
verse, quick return, automatic reverse, 
quick approach, feed left, and repeat 
continuously. 

Same as Q, feeding right. Quick ap- 
proach, feed right, quick traverse space, 
feed right, automatic reverse, quick re- 
turn, automatic reverse, quick approach, 
feed right, and repeat continuously. 

Reciprocating left and right. Feed to 
the left, stop, and feed to the right, stop. 



Reciprocating quick approach. Quick 
approach left, feed left, stop. Quick 
approach right, feed right, stop. 

Continuous reciprocating, quick ap- 
proach, full automatic. Quick approach 
left, feed left, automatic reverse, quick 
approach right, feed right, automatic 
reverse, quick approach left and repeat 
continuously. 

Continuous reciprocating, intermit- 
tent, full automatic. Quick approach 
left, feed left, quick traverse space, feed 
left, etc., automatic reverse, quick ap- 
proach right, feed right, quick traverse 
space right, feed right, etc., automatic 
reverse, quick approach left, feed left 
etc., and repeat continuously. 



Fig. 40 



44 



The Cincinnati Milling Machine Company 



Square Gibbed Bearings with Narrow Guides. — The knee 
bearing on the column and the saddle bearing on the knee have 

heavy square guides, Fig. 41, 
which are provided with 
thick, lengthwise adjustable 
taper gibs. The sliding bear- 
ing is fitted to a heavy, nar- 
row guide. The length of 
this bearing is many times 
greater than its width, which 
insures smooth movement. 
A third taper gib is provided 
for adjustment in this direction. With this construction, all 
canting or rocking on the part of the sliding members is elimi- 
nated, and the original accurate alignment of the machine is 
maintained. 




Fig. 41 

The square gibbed narrow guide. 



Overarm. — The shape of 
the work and convenience in 
chucking, frequently make it 
desirable to use the machine 
without braces. Whether or not 
this is practical depends entirely 
upon the strength of the over- 
hanging arm. In order that 
more of the work may be done 
in this way, we are fitting these 
machines with our patented rec- 
tangular overarm, Fig. 42. This 
construction enables us to make 
the arm of a heavy cross section 
to give it the necessary strength 
to do all but the heaviest mill- 
ing without the use of the 

braces. It has V bearings in the column and the arbor bearing 
supports are also attached to these same V's, thus insuring perfect 
alignment of the arbor bearings with the spindle at all times. A 
rack and pinion operated by a pilot wheel make the lengthwise 
adjustment of the overarm easy and convenient. This is an im- 
portant feature of convenience not applied to any other form of 
overarm. 




Fig. 42 

Section through the rectangular overarm 
and mechanism for adjusting it lengthwise. 



A Treatise on Milling and Milling Machines 45 



Adjustable Arbor Support Bearings. — Unless the arbor has 
a close fitting bearing in the arbor support, chatter may result, and 
it is therefore desirable to always keep these bearings closely adjusted. 
To accomplish this, we are supplying adjustable arbor bearings in the 
arbor supports, one of which is shown in Fig. 3. This bearing is 
tapered on the outside to fit the taper hole in the overarm bracket. 
There are full length slots milled on the inside and on the outside 
of the bearing. These allow the bearing to contract when it is 
drawn into the overarm bracket by means of the nut shown in 
Fig. 3. This nut is provided with a knurl which engages the small 
knurled lock nut held in place by the locking screw for locking the 
bearing in position after adjustment. Snugly adjusted arbor sup- 
port bearings contribute materially to the rigidity and accuracy, as 
well as the satisfactory operation of the machine. 

Patented Automatic Lubrication — The spindle bearings, the 
spindle drive gears and shafts, and all other rotating parts contained 
in the column are lubricated by a geared pump of ample capacity 
in connection with a reservoir at the top of the machine, from which 
independent pipes lead to the individual bearings. This pump is 
located in the pulley bracket, and is in operation at all times when 
the pulley is running. 

Centralized Oiling — In addition to the automatic oiling system 
for the mechanism in the column, described in the preceding para- 
graph, a centralized oiling system consisting of six oiling stations 
for the other mechanisms is provided. There are large oil cups on 
the saddle, the knee and the feed box. From each of these positions 
a number of bearings are oiled. The oil cups on the saddle also oil 
the table bearings, and it is not necessary to set the table to any 
specified position when oiling. They are placed at the side of the 
saddle, are never covered by the work or fixture and are so con- 
structed that the covers close automatically by their own weight. 

Cutter and Work Cooling — An eleven-gallon centrifugal pump 
is connected with the large oil reservoir in the base of the machine, 
and discharges through a %" pipe to the cutter arbor, thus supply- 
ing a large stream of cutting lubricant for cooling the cutter and 
work. Ample oil channels in the table, with an unusually large 
screened opening, return the lubricant rapidly to the reservoir in 
the base. 



46 



The Cincinnati Milling Machine Company 



The Belted Motor Drive. Any make of constant speed motor 
running at any speed between 1,000 r. p. m. and 1,800 r. p. m. may 
be used. The motor is mounted on a fixed base, fastened to the 




Fig. 43 

The belted Motor Drive. The motor is mounted where 
it does not increase the working floor space. 



machine at the rear where it does not increase the working floor 
space. The belt is kept in tension by an idler which takes up the 
slack of the belt and gives it the greatest practical amount of con- 
tact on the surface of the motor pulleys. An endless leather belt 
and a metal belt guard form part of this equipment. 



The Chain Motor Drive is similar in arrangement to the 
Belted Motor Drive shown above. The drive is by a Morse silent 
chain of ample size direct from the armature shaft to the main 
driving shaft. There are no intermediate members. The entire 
arrangement is fully enclosed in the metal belt guard which forms 
part of the equipment. Any constant speed motor running not 
slower than about 750 revolutions and not faster than 1,200 rev- 
olutions may be used. 



A Treatise on Milling and Milling Machines 



47 



Cincinnati No. 4 Vertical High Power Miller 

The No. 4 Vertical High Power Miller was designed for the heavy 
service which is required from these large powerful machines, and 

which demands greater 
strength and capacity than 
has heretofore been contem- 
plated. In this new design 
we were guided by the success 
we are having with the new 
features of our new No. 5 
Plain and Universal 
Machines, and we have em- 
bodied those features in these 
No. 4 Verticals, the most im- 
portant of which are: 

Square Gibbed Bearings 
with Narrow Guides. 
Intermittent Feed. 
All feed changes made by 
a single lever at the front of 
the knee. 

Individual Lever Control 
for all movements, both from the front and the rear of the table. 
Automatic Oiling of all mechanisms in the column. 
Centralized Oiling for other mechanisms. 
Automatic Brake for stopping spindle, etc. 
A Vertical Machine does not provide for tying the knee and the 
frame of the machine together as is the case on a Horizontal. It is 
therefore important that the knee structure and the column structure 
carrying the spindle be made amply large and strong for the severe 
strains to which they will be subjected. 




Fig. 44 

View of machine showing feed box, with 
single feed change lever and feed index at front of 
knee. 



The Spindle Head may be clamped solidly to the frame of the 
machine, giving the advantage of fixed head construction, as well 
as the advantage of a vertically adjustable head when the clamping 
screws are released. It is square gibbed, and contains both the 
upper and lower bearings for the spindle. The drive is from the 
main driving pulley through selective sliding gears to a pair of bevel 
gears on a vertical shaft which carries the back gears. This shaft 
has four integral keys, and the back gears are free to slide on it. 



45 



n Mblung Machine Compaot 




Fig. 45 

V - " ■ " ■ - ■ .l . - E - . : z±z. It: ~_I4 . --. ~ - : _ — .: : 



They ire irrinre-:: t: mesh seiezTTreiv ~:h ::: r~ : reirs :7 ::t 
sphtile Thejse reiTS ire net ke^e: :i_t:i;~ :: the sTtirtiie hi: ire 
::.-'' -1. :: :-, sle-e~e "^hizh is is hiz is the iisiirrz-e br:~rr: ::t 
spindle bearing, and its front end is keyed to the spindle itself at 
2 7777 :~:s-e t: the 7~e: beirh:^ Tr._s s".e-e"e tties ::t ir777i 
strain and leduees the bending tendency to a ininimum* and also 
relieves the spindle from torsional strains throughout its lengtii for 
i_ t ■: s:7 : is 

The Fr::e Gear. :r:".::: — i::h 7:~e: is triisziirte: :':: the 
i:~ steeh isef :':: ^1:7 :i:-e mihs is inisiihv lir-ze 7. iiirrteter 
This construction enables the maehm^ to do heavy, fast cutting 
with large cullers, smoothly and without vibration. 

Intermittent Feet 1 it eeieitii^ "irttV.e :ei7tr*e :r. these 
""ertii'.h. L^izhtiies Tie 1 : r s hit be set :':: 77" tesife-f :-v;-7 ::' 
mow^t, inebding tte«!mpWe artmnatie ^fe far whk* fl* 
...: iiiies hit :;e >e: ::: iiterrrhrtei: reeiiiz ir_ : :tt :_t7::i: 
automatic reverse at each end of the table tra t I hese : es re 
shown in Figures 39 and 40. 

Lt::::t:;::., — The eii: tteit :: the tt 
:: 1_ rih:r_s :-i72.ttt7 :':: :rrt-: it : "1:1 : 
placed in the pulley bracket provides autoi 
the running pares and meehari: 

7t7t stahris tri'hte ::::/ -z:.-zr. 11: 7.11 



A Treatise on Milling and Milling Machines 



49 



mechanisms in the knee, saddle, and table, as well as the bearings. 
It is therefore not necessary to set the table to a certain specified 
position when oiling the inside parts, nor is it necessary to remove 
the fixtures or the work. These parts can always be oiled from the 
readily accessible centralized stations. 




Fig. 46 

Machine equipped with 24" Heavy Circular Milling Attachment 

Write for Special Catalog of Nos. 4 and 5 High-Power Millers 

Milling Machine Attachments 

The range of work that a Milling Machine can do is greatly 
increased by the use of attachments. An almost endless variety of 




Fig. 47. Plain Index Head 



50 



The Cincinnati Milling Machine Company 



attachments has been devised for special requirements. It is some- 
what difficult to determine where to draw the line between what 
are essentially attachments for the machine and those other devices 
which should be properly classed as fixtures. 




Fig. 47A. Gear-Cutting Attachment 



We always carry in stock a full variety of standard attach- 
ments suitable for the various sizes of machines. In their design 
we have again followed the principle that each part of the machine 

should be equal in capa- 
city to all other parts. 

The Universal Indexing 
and Dividing Head, which 
forms part of the equip- 
ment of Universal Ma- 
chines and which can also 
be used on Plain Machines 
for work done between 
centers as well as for an- 
gular work, such as bevel 
gears, mitre gears, etc., is 
described on page 87. 

Fig. 48. 10' Plain Centers 

The Combination Index Heads. For a general line of index- 
ing work, the Combination Index Heads will be found extremely 
convenient. These can be furnished as Plain Index Centers, Fig. 47, 
indexing through a plate at the rear by means of an index lever 
mounted directly on the spindle. To this can be added the bracket 




A Treatise on Milling and Milling Machines 51 



carrying a side index plate, which makes the same divisions as our 
Universal Dividing Heads, for universal indexing through worm 
and worm wheel. This makes our Gear-Cutting Attachment, Fig.47 A, 
and the use of this can be still further extended to include spiral 
milling by adding a shaft and gears for connecting it with the lead 
screw. In this form it is the Spiral Milling Head. These heads are 
made in both 12" and 16" sizes and are recommended for use not 

sssgj^ssa^ only on Milling Machines, 



but on other machines that 
are called upon to do work 
between centers. 

Another form of indexing 
centers for small light work 
is shown in Fig. 48. These 
centers swing work 10" in 
diameter and index through 
a side index plate which 







Fig. 49. High Number Indexing Attachment 

operates through a worm and wormwheel in a manner similar to 
that employed on our Universal Indexing and Dividing Head, Gear- 
Cutting Attachment, and our Spiral Milling Head. The worm and 
wheel can readily be disengaged and the indexing may then be done 
direct by revolving the spindle by means of the handle attached to 
the disk at the rear of the head, which disk also serves as an index 
plate, and indexes any number dividing evenly into 24. The 
divisions for 3, 4, 6, 8 and 12 spaces are plainly marked. 

High Number Index- 
ing Attachment. All 

our index heads using the 
side index plate make an 
unusually large number of 
divisions, as shown in the 
table in the chapter on 
Universal Toolroom Mil- 
lers. These divisions in- 
clude all numbers, odd and 
even up to 60, even num- 
bers and those divisible by 
5 up to 120, and many use- 
ful divisions beyond these. 
However, it often happens that additional divisions are required for 
special work in the toolroom, or for model making and experimental 




Fig. 50. The Driving Mechanism 



52 The Cincinnati Milling Machine Company 



work. For all these requirements the High Number Indexing 
Attachment, Fig. 49. will be found very convenient. 

It consists of three plates of the same size and interchangeable 
with the regular side index plate. They will make all divisions, 
odd and even, up to and including 200, all even and those divisible 
by 5 up to 400. except 225-275-325-375. This is sufficient for 
practically all requirements. The indexing is all simple indexing 
direct through the plates and is therefore more desirable than any 
system of compounding or differential arrangements requiring the 
use of change gears. 

Driving Mechanism. When it is desired to equip a Plain 
Machine with a Spiral Milling Attachment and Universal Dividing 
Head., or Spiral Milling Head for a general line of spiral work, it is 
also necessary to add the Driving Mechanism shown in Fig. 50. 
for connecting the lead screw with the Spiral Head. This mechanism 
includes the 12 change gears and the segment. 




Fig. 51. Undercutting Attachment 

Undercutting Attachment. The Milling Machine is fre- 
quently called upon to cut gears of larger diameter than will pass 
under the spindle. For such work our Undercutting Attachment 
greatly extends the range of the machine. It consists of two 



A Treatise on Milling and Milling Machines 



53 



heavy raising blocks for supporting the Dividing Head, or work- 
carrying member, and a special arbor support which is attached to 
the Knee as shown in Fig. 51, instead of to the overarm, as is 
regular practice. A standard arbor and either a Universal Dividing 
Head or a Gear-Cutting Attachment can be used. The work is sup- 
ported immediately above the cut by an adjustable stud in the 

raising block under the tailstock, 
which takes the strain due to the 
thrust of the cutter, and thus relieves 
the centers from any strain from 
this source. 




High-Speed Milling Attach- 
ment. Sometimes work requires 
the use of very small end milling or 
profiling cutters which should run at 
very much faster speeds than the 
highest speeds provided on standard 
milling machines. For such work 
the High-Speed Attachment, shown 
in Fig. 52, comes in very handy. The spindle runs on ball-bearings 
and is driven through hardened gears. The attachment spindle 
speed is 3.4 times the machine spindle speed. 



Fig. 52 High-Speed Attachment 



Universal Spiral Milling 
Attachment. It is often de- 
sired to mill short lead spirals 
which have an angle that is 
greater than that to which the 
table of the Universal Machine 
can be swiveled. This can be 
easily and satisfactorily accom- 
plished by adding to the equip- 
ment of the Universal Machine, 
a Universal Spiral Milling At- 
tachment, Fig. 53. This at- 
tachment will both cut spirals of any angle up to 70°, and can be 
used on the Plain Milling Machine in conjunction with a Dividing- 
Head or Spiral Head, and Driving Mechanism for this class of work. 




Fig. 53 
The Universal Spiral Milling Attachment 



•>4 



The Cincinnati Milling Machine Company 




Fig. .54. Universal Spiral Milling Attachment 
Used as a Vertical Attachment 



short arbor IV diameter is 
supplied. The distance be- 
tween the attachment spindle 
and the bottom of the attach- 
ment is lxi". 



The spindle has a No. 10 
B. & S. taper hole and a 
draw-in bolt is provided for 
holding taper shank end mills 
or arbors in position. For 
milling racks or spirals a 




Fig. 55. Universal Spiral Milling Attachment 

Set for Angular Milling with an End Mill. 




Fig. 56. Heavy Vertical Attachment 

Vertical Attachments. There are many occasions when 
horizontal machines, both Plain and Universal, are called upon to 
do the work that could be best done on a Vertical Machine. At 
the same time there may not be enough of this to justify the instal- 



A Treatise on Milling and Milling Machines 



55 



lation of a Vertical Miller. For all such work horizontal machines 
can be converted into very efficient Vertical Machines by the 
addition of a Vertical Attachment, Fig. 56. 



Semi-High Speed Vertical Attachment. Key seating, die 
sinking, milling T-slots and work of similar character can be 

most advantageously per- 
formed with this type of 
attachment, Fig. 57. The 
cutter spindle has a No. 9 
B. & S. taper hole and is 
mounted on ball-bearings. 
It is geared two to one 
so that the attachment 
spindle speeds are just double 
the speeds shown on the index 
for the machine spindle. The 
spindle is driven through 
hardened bevel gears and can 
be set at any angle in a verti- 
cal plane, a graduated index 
being provided for this purpose. The outer arbor support of the 
milling machine provides additional support for the attachment. 




Fig. 57. Semi-High Speed Vertical Attachment 



Rack Attachments. A general line of rack cutting can be 
done on a milling machine by using a Rack Attachment, as shown 
in Fig. 58, and the usefulness of this attachment is further increased 
by the use of the Rack Indexing Attachment, Fig. 59. This at- 
tachment includes different combinations of gears which enable 
racks to be indexed by making either a half or complete turn of 
the index plate, and will index all diametral pitches from 4 to 16 
inclusive, and all even diametral pitches from 18 to 32 inclusive; 
standard circular pitches from y$ to % varying by sixteenths, also 
such odd pitches as 7 7 ", V 6 ", 7 5 ", 2 / 7 ", 7 3 ", 7 5 ". 



56 



The Cincinnati Milling Machine Company 



Slotting Attachment. 

Toolroom work, pattern 
making, and similar work 
requires the use of a slot- 
ter, but it is rarely that 
there is enough of this sort 
of work to justify the in- 
stallation of such a ma- 
chine. It can be very well 
done on a Miller by the 
addition of a Slotting At- 
tachment, as shown in 
Figs. 60-61, which has been 
especially designed for meeting the requirements of tool and die- 
makers. It can be set at an angle on either side of the vertical 
position without disturbing the length of stroke. The toolholder 
is of clapperbox construction, relieving the tool on the up-stroke. 
It may be swiveled through a complete circle and a graduated 
dial is provided for setting it at any desired angle. 




Fig. 58. Rack Milling Attachment 




Junius 

JpHlMLIIi 

dip 

Jpiniuiii 

Vi ;■:; ;i 

Igpimitr 
•Binnmit 



701 




Fig. 59. Rack Indexing Attachment 



16" — Circular Milling Attachment. This is shown in Fig. 62. 
It is applicable to Plain, Universal and Vertical Machines. It 



A Treatise on Milling and Milling Machines 



57 




Fig. 60. Slotting Attachment 



Fig. 61 

Attachment set to horizontal position for splininj. 
keyway in long sleeve. 



greatly increases the usefulness of any machine. It is driven from 
the feed box and is provided with an automatic throw-out operated by 
adjustable dogs. The direction of rotation may be reversed, which 
adapts it thoroughly for internal and external milling. 

The driving worm may be thrown out of mesh at any time when 
milling short sections of the circumference of work, and the attach- 




Fig. 62. The 16" Circular Milling Attachment 

It is also supplied as a Hand Feed Attachment. 



58 



The Cincinnati Milling Machine Company 



ment revolved by hand to bring the next surface to the cutter. 
The circumference of the attachment is graduated in degrees. 

20-inch and 24-inch Heavy Circular Milling 

Attachment 

Strength, rigidity, and simplicity are the chief factors in the 
design of these attachments. Means are provided to utilize the 
quick traverse transmission of the machine table., on the No. 4 and 



28 




Fig. 64. 20' and 24 r Circular Milling Attachment 

As used on Nos. 4 and 5 High Power Machines. 

(When used on the smaller sizes the drive is at the left, as in Fig. 62) 

Xo. 5 machines and give the attachment table a corresponding 
power quick traverse, by simply locking the auxiliary table feed 
lever at the left side of the saddle, in its neutral position. The 
power feed and power quick traverse are driven through a spline 
shaft mounted in the saddle, and a gear housing fastened to the 
end bracket of the table of the machine, from which a universal 
joint connects directly to the attachment. A single lever starts, 
stops, and reverses the power feed of the attachment, indicating 
also its direction. The power feed of the machine, as well as of the 
attachment table may be used independently, or simultaneously. 




Fig. 63. The Cam Milling Attachment 



A Treatise on Milling and Milling Machines 59 



Cam Milling Attachment. An attachment especially designed 
for milling face cams up to 16" in diameter and cylindrical cams up 
to 8" in diameter is shown in Fig. 63. The change from face to 
cylindrical cam milling is readily made by setting the wormwheel 
spindle at right angles to the milling machine spindle. It can be 
provided with a countershaft for power feeds when desired. 



INDEX BASES 

12" x 24" and 16" x 36" 



Fig. 65. The 16" x 36" Index Base 

These Index Bases, Fig. 65, are designed for high production 
work. Their application to Automatic Machines is shown in the 
illustration Fig. 65. A set of fixtures is mounted on each end of the 
base. While the pieces at one end are being milled, the operator 
replaces new ones at the other end. When the cut is finished, the 
machine automatically returns the table and the operator swivels 
the base through 180°, reclamps it, and the operation is repeated. 
It will be noted that the fixtures which are being loaded are always 
at the end of the table nearest the operator and at the point farthest 
removed from the cutters. This greatly facilitates chucking and 
adds to the safety of the operator. 

The operation of these Index Bases is as follows: 

The clamps are loosened and the plunger is withdrawn by one 

movement of the lever. The top part is then swiveled a little more 

than half way around and then brought back against plungers which 

determine its approximate location. By a single movement of the lever 



60 



The Cincinnati Milling Machine Company 




Fir -'-- 



tour. 



the index plunger is brought 
home, bringing the fixtures 
into exact ahgnment. and at 
the same time the top part 
is securely clamped to the 
base, ready for the next cut. 
The time ordinarily con- 
sumed for automatically re- 
turning the table and swivel- 
ing the Index Base is about 
6 to 9 seconds for the 12" 
x 24 size and 7 to 10 seconds 
for the 16" x 36" size. 



- -. 




F\z. -' ■ Oil Pimp for Cone-Driven Machines 



Oil Pumps. We can furnish oil pump equipments for either 
Cone-Driven or High-Power Mihers. In bo::; eases the oil reservoir 
is formed in the base of the machine and the pump is attached to 
the outside of the column, making a very neat and compact arrange- 
ment. The oil is returned to the reservoir through a flexible tube 
connected with the end of the table. These equipments are shown 
in Firs. 67 and HS. 



A Treatise on Milling and Milling Machines 



61 




4 4 6-A 



Fig. 68. Oil Pump for High-Power Machines 



Our pump and equipment for flooded lubrication are fully de- 
scribed in the chapter on stream lubrication. 




iMftw *ai 



Fig. 69. Swivel Vise 



Fig. 70. Plain Vise 



Vises. Since the work required of toolroom machines is con- 
stantly changing special fixtures are seldom used. The work is 
usually held in the vise furnished with the machine. Our standard 
design of Swivel Vise for Universal Millers is shown in Fig. 69. These 
vises are made in four sizes with jaws from 5^" wide to 8%" wide. 
They are provided with a graduated swivel base. 

They are also furnished as Plain Vises by omitting the swivel 
base, and are shown in this form in Fig. 70. 

Another standard type is the Toolmaker's Universal Vise, Fig. 
71. This is intended for toolroom work, requiring angular settings, 
not obtainable with the other styles of vises. Its jaws are 6" wide, 



62 



The Cincinnati Milling Machine Company 



ItV' deep and open SW. When in a horizontal position the top 
of the jaws are 83^" above the table. 




Fig. 71. Toolmakers' Vise 

All- Steel Vises. Our larger Plain and Vertical Machines are 

furnished with our new All-Steel Machine Vise, shown in Fig. 72. 
These larger machines are usually called upon for heavy work and 
the material comes to them in the rough state. An extremely 
accurate tool like out' standard Plain Vise, described above, is not 




Fig. 72. The All-Steel Vise (Patented) 

adapted for holding this sort of work. The coarsely serrated 
hardened jaws of the All-Steel Vise are so arranged that the clamping 
pressure causes the jaws to move downward, carrying the work with 
them until it bears solidly upon the side bars of the vise, or some 
other supporting member. 

These vises are low, and therefore hold the work as closely as pos- 
sible to the table. The movable jaw is free to swivel and thus adjusts 



A Treatise on Milling and Milling Machines 



63 




Fig. 73. Section of All-Steel Vise Showing Construction 

itself to irregular pieces. The vise is quick-acting and being made 
entirely of steel, is durable. It is made in two sizes, with jaws 8" 
wide and jaws 10" wide; 2" deep and opening 10". The vise 
is light and easy to handle. It is recommended for use not only 
on milling machines, but on other machines using vises. 



64 



The Cincinnati Milling Machine Company 




The 24-inch Automatic Cincinnati Miller 

With Intermittent Feed, Automatic Spindle Stop and Power 

Quick Return 

Plain and Duplex 
(Patent Rights Fully Reserved) 



A Treatise on Milling and Milling Machines 



65 




Fig. 74 

Showing normal spindle drive gear arrangement. 



Automatic Milling Machines 

Whenever duplicate parts are manufactured in large quantities 
as in the construction of firearms, typewriters, adding machines, 
etc., the work of the milling machine is reduced to absolute routine, 
and it has been the practice to employ a simple single purpose 
machine for the work. Since one operator must serve a number of 

these machines, it is clear 
that the more automatic 
the machines, the simpler 
the functions of the oper- 
ator, and consequently, 
the greater the number of 
machines that he can con- 
veniently take care of. 
With this in mind, the 
Cincinnati Automatic Mil- 
ling Machines were de- 
signed. 

The 24" Automatic 
The machines are of 
rigid and powerful con- 
struction. All unnecessary slides have been eliminated. There is 
no saddle. The table rests directly on the bed. When the machine 
is set up for operation, the only movable parts are the rotating 
spindle and the sliding table. A stream lubrication system, as de- 
scribed in the chapter on 
that subject, forms part 
of the equipment of each 
machine. 

The Automatic Spin- 
dle Stop. These machines 
are so arranged that at the 
termination of the table 
feed a dog will automatic- 
ally throw out the spindle 
clutch and apply the brake 
while the table is auto- 
matically reversing, so that 
the table returns while the 
cutter is stationary. This adds greatly to the safety of the operator 
and also improves the quality of the finished work. The automatic 




Fig. 75 

Arrangement of spindle drive gears for reverse speeds as used 
for face milling and also on Duplex Machine. 



66 



The Cincinnati Milling Machine Company 




= ftf.O 



B 



C 



__ ^ 



"JD 



*- 



> 



— *© 



H 






spindle stop can be easily disengaged when the nature of the work 
does not require the use of this feature. 

■ Qu,CK ««»«« The Speeds. The sixteen 

speeds included in the low series 
and the standard series are in- 
cluded with the machine. In 
order to use the high series, an 
additional pair of back gears for 
each spindle must be ordered' 
The three series of speeds and 
the gear arrangements are shown 
in Table A, (Page 67) with 
reference to Fig. 74 (Page 65). 

For Example. If the ma- 
chine is geared for 62 revolu- 
tions, reversing the gears will 
give 212 revolutions; or, if geared 
for 103 revolutions, reversing the 
gears will give 127 revolutions, 
and so on. The change gears are 
the same for each series. For ex- 
ample, gears that will give 31 
revolutions in the low series will 
give 49 revolutions in the stand- 
ard series and 110 revolutions in 
the high series. But extra back 
gears are required for each series. 
The arrangement of the spindle 
drive gearing is shown in Fig. 
74, and the arrangement of this 
same gearing for reverse speeds 
shown in Fig. 75. 

The Feed. The feed move- 
ments of the machine are opera- 
ted in the cycles shown in Fig. 
76. The fundamental cycles are: 
1. Forward quick to the 
work, feed across the work, auto- 
matically stop spindle, automatically reverse and return to starting 
point with spindle stationary. 



K 



~_Z) 



ETC 



M 



N 



ETC 



c 



5 



♦•ETC 



Fig. 76 

Diagram showing some cycles of table movement 
obtainable with the Intermittent Feeding Mech- 
anism. 



A Treatise on Milling and Milling Machines 



67 



TABLE A— SPEEDS 



REVOLUTIONS PER MINUTE 


CHANGE GEARS 


Furnished with Machine 


High Series* 


Stud D 
Outer Gear 


Stud C 


Low Series 


Standard Series 


Outer Gear 


31 
39 
51 
66 


49 

62 

SO 

103 


110 
139 
180 
232 


68 
63 
57 
51 


29 
34 
40 
46 



Speeds given below are obtained by reversing the change gears 





81 


127 


285 


46 


51 






104 


163 


367 


40 


57 






135 


212 


477 


34 


63 






170 


268 


603 


29 


68 





BACK GEARS 



Low Series 

Spindle F 59T 

Stud D 

Inner Gear 1ST 



Standard Series 

Spindle F 52T 

StudD 

Inner Gear 25T 



High Series 

Spindle F 37T 

Stud D 

Inner Gear 40T 



Proper gears for the low and standard 
series are included with each machine. 



*Back gears for providing the high series can be supplied on special order. 



TABLE B— FEEDS PROVIDED 




FEEDS IN INCHES PER MINUTE 



Low Series 



1.09 
1.36 

1.76 



High Series 



5.1 
6.4 

8.3 



CHANGE GEARS 



Shaft A 
Outer Gear 



27 
31 
36 



Stud B 
Outer Gear 



51 

47 
42 



Feeds given below are obtained by reversing the change gears 



2.4 


11.3 


42 


36 


3.12 


14.75 


47 


31 


3.87 


18.3 


51 


27 



BACK GEARS 



Low Series High Series 

Shaft A Inner Gear 59T Shaft A Inner Gear 3 IT 
Stud B Inner Gear 19T Stud B Inner Gear 47T 



Proper Gears for all of the twelve 
feeds are included with each ma- 
chine. 



68 The Cincinnati Milling Machine Company 

2. Forward quick to the work, feed across the work, quick 
forward to clear and automatically stop both feed and spindle. 
Then, when the work has been removed, the table may be returned 
quickly to the starting point by shifting the lever on the feed box. 

In both of the above cases the stopping of the spindle is auto- 
matically accomplished by tripping and applying a brake. In all 
cases, after the work is chucked, the main starting lever starts 
both feed and speed simultaneously. Under no conditions can the 
feed be engaged with the spindle stationary. 

3. If it is desired to chuck a string of pieces on the table, dogs 
can be provided to produce an intermittent forward movement, 
by which the space between pieces is automatically traversed at 
the rapid rate of 100 " per minute. This can be repeated for as 
many pieces as there are on the table. 

A number of variations of the above fundamental cycles may 
be obtained by the use of additional dogs. A full representation 
of the most useful cycles is given in the accompanying diagram, 
Fig. 76. 

Twelve feeds from 1.09* to 18.3" are provided. These are in 
two series as shown in table B. Feeds are given in inches per minute. 

It will be seen that should a feed of 1.09* be selected, then by 
reversing these feed gears, 3. 87" feed will be obtained. In the 
same way, reversing gears for 1.36" feed will give a feed of 3.12". 
and so on. The feed gears are the same for both series. But dif- 
ferent back gears are required for each series. 

The 48 -inch Automatic. In these machines we have followed 
closely the design which has proven successful in our 24" Automatic 
Millers. These larger machines are built as Plain, Duplex and 
Widened Bed Duplex Machines. They are manufacturing millers 
designed for heavy work, introducing into this new field the 
economies and rapid production which Cincinnati 24" Automatics 
have effected for work within their range. 

Speed changes are made through change gears. The avail- 
able spindle speeds are shown on the speed plate. The machine 
equipment includes change gears for eight speeds. 

Intermittent Feed with a power quick traverse of 150" per 
minute provides fourteen dog-controlled cycles of operation, shown 
in the diagram Fig. 76. A single lever, having four positions, controls 



A Treatise on Milling and Milling Machines 



69 




1459 



48 -Inch Automatic Duplex Cincinnati Millers 
With Constant Speed Drive and Intermittent Feed 



(Patent Rights Fully Reserved) 



70 The Cincinnati Milling Machine Company 



both the feed and the power quick traverse. The direction of the 
lever indicates the direction of the table movement. For example. 
moving the lever to the left causes the table to travel in that direc- 
tion. An overload releasing device protects the feed and quick 
traverse mechanisms. 

Feed Changes are made through change gears. The eight 
feed change gears furnished with the machine provide sixteen feeds. 
The arrangement of the change gears for any selected feed is shown 
on the feed plate of the machine. 




Fig. 77 



The 4S r Duplex miffing two rows of motor frames, iH' wide. 
-£. :V :eei. Txe ixr-xre; ire z:-:e: :_=. :r_e 1:' x E:' IxiLtz 
Base, and the iuUauuifc tenl feed is used. Production, 130 pieces 

per hour. 

The Structure. The Machine is composed of a minimum 
number of units. The table rests directly on the solid bed which 
also supports the spindle head and tailstock. There is no saddle. 
The cross adjustment is made through the spindle head. An over- 
hanging arm aligns the spindle and the outer arbor support. In 
order to provide a machine of great strength and rigidity, structure 
has been unified by connecting the headstocks on the Duplex, and 
the headstock and tailstock on the Plain by a heavy top bar. 

Power is transmitted through a train of hardened steel gears 
and hardened shafts. The starting lever is conveniently located 
with the feed and quick traverse lever at the operator's working 
position. Disengaging the clutch brings the spindles to an instan- 
taneous stop through the operation of an automatic brake. This 
feature is not dog-controlled as on the 24" Automatics. 



A Treatise on Milling and Milling Machines 71 




The 18-inch Plain Manufacturing Cincinnati 
Miller with Constant Speed Drive 



(Patent Rights Fully Reserved) 



72 The Cincinnati Milling Machine Company 



18-inch Plain Manufacturing Miller with 
Constant Speed Drive 

This is a simple machine of the column and knee type, designed 
for the rapid production of small machine parts as used in the 
construction of typewriters, sewing machines, adding machines, 
registering machines, etc. 

Evidence of its rigid construction is very clearly furnished by 
the illustration. The drive is by single pulley, direct from the 
line shaft. The machine has 12 speeds, from 30 to 600 r. p. m., 
and four feeds, driven from the spindle, ranging from .011" to 
.032" per revolution of spindle. 

Quick-Acting Operating Arrangement. The operator from 
his position in front of and at the left-hand end of the table con- 
trols the feed movements with his right hand. Assuming a piece 
of work placed in the fixture, he moves the table forward at the rate 
of 2%" per turn of handwheel until the dog hits the trip, which 
automatically engages the power table feed. At the end of the cut 
a second dog disengages the table feed and stops the table, which 
is then returned to the starting point, bringing the fixture immedi- 
ately in front of the operator who, after a new piece has been chucked, 
repeats the above movements. 

An analysis of these movements compared with usual practice 
will show that the operator's work has been simplified and many 
of the usual time-consuming elements are eliminated. He may 
move the table forward as rapidly as he wishes, and he need not slow 
down when he approaches the cutter because the trip removes all 
need of precaution. 

Therefore, with the dog properly set, the work is brought rapidly 
close to the cutter before the power feed is thrown in, thus reducing 
the actual feed distance to very little more than the actual amount 
needed to traverse the work. 

Both of the foregoing machines have proven very popular with 
managers because they increase output, and with operators, because 
they very materially reduce labor. 



A Treatise on Milling and Milling Machines 73 




Cone-Driven Plain Cincinnati Miller 
Made in Four Sizes 

(Patent Rights Fully Reserved) 



The Cincinnati Milling M, 



V - _ T-" 



CHAPTER II 

ERECTION. CARE AND ADJUSTMENT OF 
MILLING MACHINES 



Erection. Although the Milling MapJiing is a self-contained 
:-aaae r it is desirable that it be set on a soMd floor. It is important 
[ it be set level and it is best when setting up a machine to place 

vol :u t::t uablo. and :hon ~hh uuiuaary shuah.es. ~t::t under 
base aoarll ahe uabh shi^s level. Shuazles should ::o: bo :d-o: 
t the base round so that the weight of the machine will 

iisuhbuoed :vor ::o oo'o ba,se. 



The Countershaft. The 1 



shaft for Cone-Drrren Ma- 
urly as possible directly over 

'. hear :he oo::u:uou an, 
luauaoershazb is Ioto! 
^ a e ~u us aru u u a . 1 



_•,. 




It is of the disk clutch construction and always has a driving 
capacity considerably in excess of the power required by the macLhae . 
When wear does take place it is easily adjusted. The clutch dish is 
placed on the shaft so as to face the disk on the pulley. The holder 
for fingers is screwed to the body of the disk, the ends of the fingers 
reaching over the disk on the pulley. Wear is taken up by first 
loosening the clamping screws and then screwing the holder for fingers 



A Treatise on Milling and Milling Machines 75 

on the clutch disk away from the pulley. Make sure that the screw 
is again tightened after the adjustment has been made, to insure 
that the holder for fingers will be tightly locked to the clutch disk. 




Fig. 79. Detail of Countershaft Clutch 

Constant Speed Drive High-Power Machines are not fur- 
nished with a countershaft, but are driven direct from the line. 
Care should be taken when belting up the machine to be sure that 
the pulley runs in the direction indicated by the arrow on the 
pulley. A suitable pulley should be placed on the line shaft to 
drive the machine pulley at the proper speed. In determining the 
size of this pulley, follow this rule: 

Revolutions of machine pulley multiplied by the diameter of 
machine pulley, divided by the revolutions of line shaft, equals diameter 
of pulley on line shaft. 

For Example. Assuming a line shaft running 200 r. p. m. and 
a machine pulley 20" diameter running 325 r. p. m. Then, we have — 

325 r. p. m. x 20 
200 

line shaft. 



= 323/2" for the diameter of the pulley on the 



This same rule, of course, applies when determining the size 
of the pulleys on the line shaft when driving a countershaft, except 
in this case we multiply the speed of the countershaft by the 
diameter of its pulley and divide by the revolutions of the line shaft. 

Oiling. It is important that a Milling Machine be well oiled. 
We advise the use of a good grade of mineral oil. On all our machines 
the oiling places are plainly marked and those places provided with 



76 



The Cincinnati Milling Machine Company 



oilers are all in plain sight. The operator should acquaint himself 
with all of them and be careful not to neglect any. 

On our High-Power Machines sight-feed oilers are used for the 
important bearings, and most of the mechanism is oiled from central 
oiling places. These should be filled once a day. The table bearings 
are oiled through oil holes provided on the front and rear sides of 
the table. To oil the inside parts of the saddle, bring the zero line on 
the table over each one of the three lines on the saddle and in each 
case oil through the oil hole over the zero line on the table. 
Be sure to keep the table in each of these positions long enough to 
give the oil time to pass through the tube to the place to be oiled. 




LOCKNUT FOR ADJUSTING SPINDLE. 

Fig. 80 

Section through driving gears and spindle of a High-Power Machine. 



To Remove the Spindle from the Machine. This is an 
operation that is rarely necessary. When, after long and hard use, 
extensive overhauling makes this advisable, it is only necessary 
to loosen the lock nut on the Spindle, Fig. 80, at the same time driv- 
ing the spindle forward. After the spindle has passed through the 
main gear at its front end on both Cone-Driven and High-Power 
Machines, it will come out freely. On the Nos. 4 and 5 Machines 
with rectangular overarm and also on the M-type Nos. 1 and 2 
Machines the lock nut at the rear of the spindle must first be 
loosened, then proceed as above. 



A Treatise on Milling and Milling Machines 77 

Adjustments. The machine spindles are tapered at the front 
end, and are so proportioned that under ordinary service the wear 
on the end thrust collars and on the spindle bearing proper is about 
equal, so that by screwing the lock nut on spindle against the front 
box, the spindle is drawn into its taper bearing to proper adjust- 
ment. All machines are properly adjusted before they leave the 
factory, and this readjustment is seldom necessary. When the 
spindle adjustment has been properly made, the machine should 
again run without further adjustment for a number of years. 

The white metal thrust bearing of the spindle rests against 
thin washers of hard paper. By removing some of these or adding 
additional ones, as the case requires, an independent adjustment 
of the thrust bearing can be made when excessive continuous service 
on one kind of work may make this advisable. 

Care of the Machine. The machine should be kept clean. 
This point can not be emphasized too strongly. The continued 
accuracy and durability of the machine depends upon this more 
than on any other one thing. All oil holes should be kept closed, 
and it is advisable when oiling to first wipe iron dust and chips 
away from oiling places before inserting the oil can. After a bearing 
has been allowed to run dry due to insufficient or improper oiling, 
and has become cut, any amount of flooding with oil will not improve 
its condition. It is best, therefore, to exercise proper care in the 
first place. 

When oil holes or oil tubes become clogged with gummy oil they 
should be thoroughly flushed with gasoline. This will not injure the 
bearings, but will have a cleansing effect which will insure that all 
bearings will again get their full supply of clean oil. 

The machine should never be taken apart unless absolutely 
necessary, and then the work should be done by a competent man 
who has first familiarized himself with the construction of the 
machine. To remedy some temporary trouble, it seldom is neces- 
sary to take any great portion of the machine apart. For example, 
trouble due to an improperly oiled bearing may always be located 
by turning the various members of the mechanism by hand until 
the injured member is located. By bearing these things in mind a 
great deal of the time and trouble required to dismantle a machine 
may be saved. 



78 The Cincinnati Milling Machine Company 

The careful workman will see to it that wooden coverings 
are provided for the front of the knee and the top of the 
table, so that he may place work or tools on these parts without 
injury to the slides or to the upper surface of the table. Attention 
to this will do much to maintain the original accuracy of the machine. 

When ordering repairs always give us the construction num- 
ber and letter stamped on the front face of the column immediately 
below the front box of the machine. Also, specify the part wanted 
by number. We have for some time past numbered every part 
entering into the construction of our machines, and these numbers 
are placed where they are not liable to be obliterated by wear. 
By specifying the part number in each case, making replacements 
will be very much facilitated. 



A Treatise on Milling and Milling Machines 



79 




Fig. 81 



Names of Parts of Cincinnati High-Power 
Plain Millers and Their Use 

These illustrations show the location on the machine of the 
different parts referred to in this book. They will contribute to 
a better understanding of the machine and also facilitate ordering 
repairs. Numbers in circles are on the part to which they refer, or 
they are directly over that part when it is concealed. 

1. Clutch lever for starting and stopping machine. 

2. Table feed setting lever. 

3. Power quick traverse operating lever. 

4. Table feed adjustable trip dogs. 

5. Table feed trip plunger. 



80 The Cincinnati Milling Machine Company 

6. Cross and Vertical feed setting lever. 

7. Vertical and cross feed lever. 

8. Lever for operating feed when standing behind the table. 

9. Cross feed trip plunger. 

10. Cross feed adjustable trip dogs. 

11. Cross adjustment hand wheel. 

12. Vertical adjustment crank. 
13-14. Quick traverse limit stops. 

15. Feed change levers. 

16. Pilot wheel for operating feed change tumbler. 

17. Feed index plate. 

18. Speed change levers. 

19. Pilot wheel for operating speed change tumbler. 

20. Speed index plate. 

21. The treadle for giving the gears slight motion to facilitate 

speed changing. 

22. Guide for Vertical feed trip dogs. 

23. Vertical feed, adjustable trip dogs. 

24. Vertical feed trip plunger. 

25. Ball crank for longitudinal table adjustment. 

26. Micrometer dial for longitudinal table adjustment. 

27. Rack on main clutch rod. 

28. Quick traverse driving belt. 

29. Bracket containing left-hand bearing for table feed screw. 

30. Driving keys in flanged spindle end. 

31. Oil pot. 

32. All steel vise. 

33. Bushings in arbor bearings. 

34. Table feed operating lever (concealed behind the braces in 

Fig. 81. See Fig. 82.) 

35. Telescopic elevating (Vertical feed) screw sleeve. The Vertical 

screw (35-A, Figs. 82 and 83) is inside of this sleeve. 
35-A. Vertical feed screw (Fig. 82). 

36. Outer arbor bearing support which can be bolted to the braces. 

37. Intermediate arbor bearing support. 

38. Outer support, for short arbors having a bearing on the out- 

side of the nut. (Arbors style A, B, C, G, page 115.) 

39. Adjustable bronze bush for arbor bearing. 

40. Braces for tying the overarm, outer arbor support and knee 

together. 

41. Overarm. 



A Treatise on Milling and Milling Machines 



81 




42. Column of the machine. 

43. Drive box. 

44. Feed box. 

45. Driving pulley. 

46. Feed reverse box. 

47. Saddle. 

48. Table. 

49. Knee. 



Fig. 82 
50. 

51. 



52. 



53. 



Base. 

Bracket containing right- 
hand bearing for table feed 
screw. 

Bridle by which the braces 
are fastened to the knee. 

Front spindle bearing box. 



82 The Cincinnati Milling Machine Company 

54. Front face of column where the construction number and 

letter will be found. Always give us this number and letter 
when ordering attachments or repairs. It identifies the 
machine. 

55. Micrometer dial for vertical adjustment. 

56. Micrometer dial for cross adjustment. 

57. Front sliding covers in top of knee. Back sliding covers cor- 

responding with these can not be seen. 

58. Cross screw bracket at front of knee. 

59. Trip plunger bracket. 

60. Adjustable gib for table bearings. 

61. Adjustable gib for saddle bearings. 

62. Telescopic Universal joint shaft (long fork). 

63. Universal joints (short forks and ball in fork). The short fork 

connecting with the shaft in reverse box has a flange which 
carries the shearing pins (safety fork). 

64. Oil pump connection with tank which is in the base of the 

machine. 

65. Ejector rod. 

66. Vertical feed nut on base of machine. 

67. Location of oil pump when furnished. 

The following parts are shown in Fig. 82: 

68. Power quick traverse pulley. 

69. Quick traverse bracket on column. 

70. Long fork on quick traverse shaft. 

71. Extension shaft, quick traverse. 

72. Cover over end of lead screw. (Remove when setting up for 

cutting spirals.) 

73. Short forks of Universal joints. (These are identical with 

the forks used for driving the feed.) 

74. Quick traverse bracket under saddle. 

75. Quick traverse operating lever bracket. 

76. Quick traverse lever shaft. 

77. Quick traverse safety lever. 

78. Cover over driving gears. (Remove when oiling inside parts.) 

Additional Parts Applying to Vertical Machines Fig. 82 

79. Pilot wheel for quick adjustment of spindle (6" per torn). 

80. Knob for engaging hand feed movement. 

81. Handwheel for hand feed movement. 

82. Micrometer dial for hand feed movement. 



A Treatise on Milling and Milling Machines 



83 




101 72 



Fig. 83 

83. One of four bolts for clamping spindle head solidly to frame 

of machine for heavy work. 

84. Spindle head. 

84-A. Rack for adjusting spindle head. 

85. Lower spindle bearing box. 

86. Upper spindle bearing box. 

87. Head adjustment worm casing. 

Additional Parts Applying to Universal Machines Fig. 83 

88. Arbor. 

89. Universal Indexing and Dividing Head. 

90. Tail stock. 



84 The Cincinnati Milling Machine Company 

91. Elevating center for tailstock. 

92. Front index plate on spindle for direct indexing low numbers. 

93. Head center. 

94. Driver for dog. 

95. Side index plate. Drilled both sides, reversible. 

96. Sector for convenience in indexing. 

97. Index pinholder. 

98. Index pin (in the holder). 

99. Segment for change gears. (This segment with a complete 

set of change gears constitutes a Driving Mechanism.) 

100. Swinging arm or bracket for idler gear. 

101. Change gears for cutting spirals (12 in a set). 

102. Idler gear. 

103. Quick return crank handle. 

104. Swivel carriage or housing. 

105. Vise body. 

106. Swivel base for vise. 

107. Holder for adjustable bronze bush for outer arbor support. 

(This is substituted for the large bearing holder in the 
intermediate arbor support.) 

108. Steady rest. 

109. Universal Milling Machine chuck 

110. Vise housing. 

111. Vise screw. 

112. Vise jaws. 

113. Swivel block in tailstock. 

114. Tailstock center carrier. 

115. Saddle of Universal Machine. 

Additional Parts Applying to Cone-Driven Machines 

116. Cover over back gears. 

117. Cover over back gear pinion. 

118. Back gear quill. 

119. Back gear operating lever. 

120. Back gear locking pin. 

121. Driving cone. 

122. Back gear sleeve. 

123. Back gear shaft. 

124. Braces as used on Nos. 1, 2 and 3 cone-driven machines. 

125. Bridle for attaching braces to knee. 



A Treatise on Milling and Milling Machines 85 




Cone-Driven Universal Cincinnati Miller 
Made in Three Sizes 

(Patent Rights Fully Reserved) 



86 



The Cincinnati Milling Machine Company 



CHAPTER III 



UNIVERSAL TOOLROOM MILLERS 



The term "Universal" designates a Miller especially designed 
for automatically milling spiral forms. 

This, in addition to its equipment for cutting spur, mitre and 
bevel gears, and doing a general line of indexing and other work 
that is held between centers, makes the Universal Miller the gener- 
ally accepted toolroom machine. 

Such machines have the table mounted on a swiveling carriage, 
permitting the work held between centers to be set at an angle with 
the cutter to suit the spiral being milled. 

Their equipment includes a Universal Dividing Head, change 
gears, chuck, etc. These two particulars, viz., swiveling table and 
Dividing Head equipment, constitute the only difference between 
Universal and Plain Millers. 

The development of 
modern machinery has 
brought with it the use of 
spiral gears of wider angles 
than that to which the table 
of a Universal Miller can be 
swiveled. 

To meet these require 
ments we brought out our 
Spiral Milling Attachment 
some years ago to increase 
the range of Universal 
Millers to take in this work. 
Since then we have ar- 
ranged our Plain Millers so 

that they can be used with Fig - 84 - PIain MiUer Equipped for Cutting Spira,s 

the Dividing Head geared to the table feed screw for generating 
spirals, the same as Universal. By adding to this equipment the 
Spiral Milling Attachment, Cincinnati Plain Millers will cut spirals 
of greater angle than can be cut on any Universal Miller with regular 
equipment. 




A Treatise on Milling and Milling Machines 87 



In recent years Plain Millers have been coming into more general 
use as toolroom machines than formerly, it being recognized that 
only a portion of toolmaking consists of spiral work and for all other 
purposes the Plain Machine has the advantage of greater rigidity. 
For a small toolroom using only one machine, it is customary to 
select a Universal. Additional machines may be Plain or Universal 
in proportion to the amount of spiral work to be done. It should 
be borne in mind that our Plain Millers are made to the same close 
limits of accuracy as our Universals. 



e^i 




Fig. 85. The Dividing Head 

This is the most important feature of a Universal Miller 

Toolroom machines are not often required to do heavy cutting. 
Extreme accuracy is more essential than great power. But in order 
to produce accurate results, it is essential that all the working parts 
of these machines be as rigid as it is practical to make them. This 
is especially important in regard to the large sliding members of 
the frame — such as the table, saddle, knee and column. On our 
machines these are constructed on the enclosed box principle, all as 
detailed in the preceding pages describing Plain Machines. 

We have based our design of each of these members on a definite 
knowledge of the nature of the strains to which it is subjected. 



The Dividing Head 

A modern, powerful Universal Miller is severely handicapped 
unless it is equipped with a Dividing Head that is strong enough to 
do work commensurate with the capacity of the machine itself. 



s> 



The Cincinnati Milling Machine Company 



The construction of ours is shown below. The worm and worm- 
wheel are unusually large, and when, after long service, wear does 
take place, it can be quickly taken up by means of the adjust- 
ing screws shown in Fig. 87. These screws are made accessible by 
simply removing a cover which encloses the worm casing. Thus the 
adjustment can be made when necessary without taking the head 
apart, and in the same manner and to the same degree of nicety as 
it is done in our shop when 
-':.- hea ::s are ±~s: asseri- 
:..-."_. ana zisza. The ?..::- 
yi5~zr.~z.~- :':r ~ear is made 
:z. a s::a:^a: ..a - z~~z~il- 
dieular tolL axfe tftte ■ 
~::a:~aeal. :ae w:m :as- 
inr D-5-ir.z ::adaei car^e-en 
t- mM ~*-, -*. ^^ 

SC-. Raaaa:eaai;ui— r— s 

io r.c~ Tar:~ tiaa ~:m 

and wormwheel out of alignment, and therefore do not affect the 

accuracy of the mechanism. 

The work spindle is large in diameter and its bearings are adjust- 
able for wear. It is provided with a clamping device. Fig. 90, by 
means of which it can be firmly locked during cutting operations 
without disturbing the accuracy of the spacing. This relieves the 
worm, the wormwheel and index pin from all strain, thereby avoid- 
ing unnecessary wear. 






WS 



, f-;-- -^ 



ji 



A. 




ADJUSTING SCREWS 

Fir. ;7 



WORM CASJNS 



A Treatise on Milling and Milling Machines 



89 



It will be noted that the front bearing tapers toward the front 
END. The effect of the clamp therefore is to take up whatever play 



CLAMPING STRAP 




ADJUSTING SCREWS WORM CASING 

Fig. 88 



exists by pushing the spindle forward in its bearing and thus bring- 
ing it into perfect alignment before actually clamping it. 

The spindle may be set at any angle from 5° below the horizontal 
to 50° beyond the perpendicular position. The swiveling block is 



CLAMPING R\NG*0R 
LOCKING SPINOLE 



SWIVEL BLOCK 



BOLT FOR 

CLAMPING SWIVEL 

BLOCK 




WORM CASING 



Fig. 89 



graduated about its circumference and provided with a vernier 
reading to five minutes, or iV of a degree. The swiveling block 
swings on large trunnions (6H" diameter on 10" head and 8%" on 12 " 



90 



The Cincinnati Milling Machine Company 



and 14" heads), clearly shown in the illustrations, and may be held 
rigidly at any angle by clamping the large trunnion bearings by 
simply tightening two cap screws. The rigidity with which the 
clamps hold the trunnions is carefully tested, Fig. 91, on each head 
as soon as the swivel block and clamps have been fitted. 




g 536-1 



HORIZONTAL SECTION OF CINCINNATI DIVIDING HEAD. 



Fig. 90 



The spindle clamp consists of a split ring, C, which is spread by the wedge 
B by tightening the screw A, thus clamping the spindle endwise, securely, 
without crowding it out of alignment. 

Every head must carry 600 pounds 22 inches from the center of 
the swivel without any evidence whatever of failure on the part of 
the clamps to rigidly hold the swivel block in position. 




Fig. 91. Test of Rigidity of Clamps 

Note the simplicity of our clamp: the large clamping surface; and 
that the swivel bearing is completely protected. This insures that 
it will not become injured so as to destroy the alignment of the head. 

In addition to cutting spirals, the Dividing Head is especially 
adapted for bevel and mitre gear cutting as described in the special 
chapter on that subject. 



A Treatise on Milling and Milling Machines 



91 



Work of this sort should always be done with the Dividing Head 
spindle set at an angle away from the direction of the cut, so that 
any springing that may result from the small arbors that the 
nature of such work often requires, will be away from the cutter 
and prevent its gouging in. This requires that the spindle be set 
past the vertical position. Ours can be set to 50°. It also requires 
a head of the greatest rigidity. The details of ours are all very 
large, and the test on the preceding page shows how securely our 
spindle is held. 

The Dividing Head Tailstock. The tailstock has an adjust- 
able center bar which may be raised and lowered through rack and 
pinion. It is carried in a slide which can be swiveled to 10° above 
or below the horizontal to bring the centers in line with the center 




Fig. 92 

An example of accurate indexing. 

of taper work. It is so constructed that the cutter can pass over it 
without injury when set at an angle. It is provided with two 
centers, one for small light work and the other for heavy work, 
and may be reversed to bring either in position. 

The centers are carried in a massive slide which has V-bearings 
in the housing. The clamping bolt passing through the latter 
serves as a journal about which both the housing and the slide 
carrying the centers revolve. 



92 



The Cincinnati Milling Machine Company 



TEST SHEET FOR DIV. HEADS 



Center runs true on point 



.000 7$, 5 




Some Evidences of 

Dividing Head Accur- 

v acy. The accompanying 

Shop Qx&*J0<?-A- - .Sue.. . /JS... - Div. Head Number***- OTTfT ■,..-,. 1 . , . 1 

Date a^Tw x^^^ dividing head test records 

Assembler's Number. 4Z 3, Name ^ S^ «^>-V^£ WC^ draWn at TandOm 

Date Inspected ^/£///6 Inspector. W^/?^^^^<^^^._^ from OUr fileS. They TC" 

present average accuracy. 
They are only a few of the many 
similar tests which every one of 
our Dividing Heads must pass. 

We call special attention to 
the indexing test. This puts our 
regular product in the same class 
with instruments of precision. 

We are able to accomplish 
this because of special worm and 
wormwheel generating machines 
and other special tools which we 
Fig. 93 have developed for this work 

Test of accuracy of Dividing Head Center. aloTlP 

Fig. 92 is an example of the accuracy of our index mechanism. 
Six Y diameter holes are spaced equally on a circle 14 3^ " in diameter. 
They are first drilled, then bored to size. The maximum radial 
error is less than two ten 
thousandths (.0002) inch, 
and the maximum chord- 
al error is less than three- 
quarter thousandths 
(.00075) inch. The radial 
measurement is made 
from the centrally placed 
standard plug gauge and 
read from the lead screw 
dial in the usual way and 
finally checked with mi- 
crometer calipers. 

This extreme chordal 
accuracy (that is, the ac- 
curacy from hole to hole) 
results directly from the 94 

aCCUraCy Of the 12" index Test of accuracy of alignment. 



TEST SHEET FOR DIV. HEADS 



Spindle in line with tee slot 
Spindle 



table it outer end of II' test bar 
tral with tee slot in table front or back 



] Maximum Error ITest ©Thousandths 
Allowed ., 



""' t QOl" 



. Head Numbef^r2"13^^^ 

/ / 9/G> _ 

Number "^fV «P Name <Cr(, ~C&*HL4L4&*. _ 

/&/ Z. / / /C Inspector \J0yLJz4t£*l*-L^f u &. 

/" / ft 389-6 



Shop Order ..7.<00%L Size / £, 

Date Assembled <^ &4ttU*2sry 



Date Inspected < 




A Treatise on Milling and Milling Machines 



93 



head on which the work is done. The data given with the indexing 
test show why our index heads can do such work. 

Accurate indexing can not be done, no matter how accurate the 
index mechanism, unless the dividing head is made to close limits 
in other particulars. To give a better understanding of the care 
we take in testing out each part, a few of our methods are shown. 

If the center does not run true you can not do accurate work of 
any kind between centers. Ours are all tested by revolving the 
spindle with the indicator resting against the point of the center, 
Fig. 93. 

This test is repeated after the center has been removed, turned 
part way around and replaced. The record shows a total error of 
one-quarter thousandth (.00025) inch, that is, one-eighth on each 
side of the true position — too small an error to affect work usually 
done on a Miller. 

The alignment test, Fig. 94, insures that their spindles are in 
close alignment and central with the T-slots of the Miller table. 

Readings taken along one side of the 18" test bar show the parallel 
relation with the T-slots. The central relation with the T-slots is 
shown by the difference between readings on both sides of the test 

bar. The record shows a 
total "error found" of one- 
thousandth (.001) inch in 
each case. That's accurate 
enough for the most exact- 
ing requirements. 

Fig. 95 shows how the 
indexing accuracy of the 
wormwheel is tested in the 
finished head. The 12" 
disk contains an accurate- 
ly graduated silver ring. By 
means of a microscope with 
a micrometer adjustment, 
we can read the errors in the wormwheel and also those in the worm, 
to one-fortieth of a thousandth (.000025) of an inch; not only the 
errors in pitch, but also the inaccuracies of the tooth face. 

A piece of accurate indexing is shown in Fig. 96. Thirty-six 
holes, y± diameter are spaced on the periphery of a 19" disk, rigidly 
held on a 12" index head. They are first drilled and then bored a 




Fig. 95 

The indexing test. 



94 



The Cincinnati Milling Machine Company 





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trifle under size, and finally reamed to a plug gauge fit with a 
specially ground V' end mill. The error between holes is less than 

one thousandth (.001) of an 
inch. In addition to illus- 
trating the accurate results 
that can be obtained, this 
also shows the best method 
of handling work of a larger 
diameter than the index cen- 
ters will swing. 

Fig. 97 shows the use of 
the Dividing Head for index- 
ing a drill jig. This jig has 
12 holes distributed over all 
of its sides. Some are radial, 
and some are at an angle. 
By holding it between cen- 
ters, the spacing and the 
fig- 96 angles are obtained by a 

combination of movements; circumferentially, by indexing; at an 
angle with the radius by indexing and vertical adjustment; and 
lengthwise by means of the lead screw. The lengthwise and vertical 
measurements are checked by micrometer calipers in the usual way. 
They show an accuracy with- 
in one-half thousandths 
(.0005), inch but the accuracy 
of the circumferential spacing 
results entirely from the ac- 
curacy of the index, and 
comes within one-tenth of a 
degree or six-tenths of a 
thousandth (.0006) inch on 
this diameter of 7". 

Fig. 98 shows a piece of 
work that requires a machine 
that is not only extremely Fig. 97 

accurate, but must be in correct adjustment throughout. The 
disk is 18" in diameter when finished and has five slots evenly 
spaced. The sides of the slots are radial and must be finished 
individually. The maximum variation in the distance between slots 
is not over one thousandth (.001) inch. 



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A Treatise on Milling and Milling Machines 95 



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Care and Use of the Dividing Head 

The preceding illustrations show that the Dividing Head is in 
reality a precision tool. We go to unusual expense to make it 
accurate, and this is a large factor in the cost of the Universal 
Machine. But all this accuracy and refinement can be lost in a 
short time if the Dividing Head is not properly taken care of. It 
should be kept well oiled with a good grade of mineral oil. It should 
be kept clean and it should never be placed on the floor, but a suit- 
able bench or shelf should be provided for it. In fact, when not in 
use, it should be given the same care and protection that is given 
other precision tools, gauges and instruments. 

Even the most accurate Dividing Head will not produce accurate 
work unless the conditions under which the work is done are correct. 
For instance, it sometimes happens that a gear is to be cut very 
accurately and dependence is placed on the Dividing Head alone, 
without taking proper care that the machine is adjusted, that the 
work is held properly, that the cutters are in good condition, etc., 
resulting in disappointment in the finished piece of work. In such 
cases the blame may very often be improperly attributed to the 
Dividing Head. 



96 The Cincinnati Milling Machine Company 

Where to Look for Cause of Errors. An understanding of 
those things which cause inaccuracies will readily point the way to 
a remedy. We have had complaints in which the proof submitted 
to show the inaccuracy of the Dividing Head was that after the gear 
had been cut, the cutter would not pass through the first space 
without removing metal from one side or the other. When we 
remember, that after having indexed through a full revolution, 
exactly the same points of the indexing worm and wormwheel are 
in contact that were in contact when the first slot was cut, it is 
evident that no matter how inaccurate these members might be 
the piece of work will come back to exactly the same position in 
relation to the cutter. It follows therefore, that the conditions 
above mentioned are positive proofs not of inaccuracies of the 
Dividing Head, but that the trouble is somewhere else. Either 
the work slipped on the mandrel; the mandrel did not run true; 
the driver had play; the milling machine was out of adjustment; 
the indexing had not been properly done; or, the cutter was dulled 
on one side. 

The Milling Machine spindle must be in close adjustment end- 
wise; otherwise, its end motion will change the relation between the 
cutter and the centers of the Dividing Head and produce inaccurate 
work. The same thing will happen if the table gib is not properly 
adjusted. The usual result of these faults is thick and thin teeth 
in the gear being cut. If the work slips on the mandrel, accurate 
work can not be produced and the same is true if there is any play 
between the dog and the driver. In the same way, it must be clear 
that if the mandrel does not run true on centers, the gear blank 
will wobble and this wobbling may be sufficient to cause greater 
errors than are permissible on the finished work. If the cutter is 
dull, especially if it is duller on one side than on the other, it is likely 
to crowd the work sufficiently to produce inaccuracies for which 
neither the Dividing Head nor the machine is to blame. 

It is sometimes thought by Milling Machine users that inac- 
curacies in the side index plate are to blame for large inaccuracies in 
the finished work. This is not likely to be so, because the ratio 
between the worm through which the index operates and the worm- 
wheel is 40 to 1. Therefore, the error in the finished work due to 
this cause can not be more than one-fortieth of the error between 
the holes in the index plate on a circle the same diameter as the 
circle on which these holes are drilled. Inaccuracies in indexing 
frequently result from the back lash not being properly taken up. 



A Treatise on Milling and Milling Machines 



97 



How to Set Up for Indexing a Gear. When an accurate piece 
of indexing is to be done, a Dividing Head that is in good condition 
should be placed on a machine that is in similarly good condition. 
Then care should be taken to see that the machine is in proper 
adjustment in all respects, such as end play in the spindle, looseness 
in the table, saddle or knee gibs, etc. The arbor should be in good 
condition and properly held in the spindle of the machine; the 
cutter should be placed as near the shoulder of the arbor as the work 
will allow, and the cutter must be sharp. The Dividing Head 
must of course also be in proper adjustment; then, with the Dividing 
Head in place on the machine the cutter must be properly centered 
with the Dividing Head center. Then, with the work securely 

mounted on a mandrel, which 
itself runs true, and properly 
secured between centers with 
no play between the dog and 
the driver, we are ready to 
proceed. 

The Dividing Head must 
be set with the indexing 
pointer in place for the 
proper number of divisions, 
and the sector must be set 
for the proper spacing, as 
described a little later. The Dividing Head spindle must now be 
clamped. 

The machine should be started and the gear blank should be 
adjusted vertically until there is evidence that the running cutter 
touches it. Then it must be moved aside and the knee raised 
vertically for the proper depth, as shown by the dial, and we will be 
ready to take the first cut. 

After this has been taken we loosen the clamp, and index for the 
next tooth making sure that the pointer moves in one continuous di- 
rection. If, by any chance, it passes the hole, we must return some dis- 
tance and again come forward and let the pin touch the plate a little 
before it enters the hole. In this way we will be sure that all the 
back lash is taken up. We then clamp the spindle and proceed with 
the next cut, and so on. 

The various methods of indexing, the use of the sector, and 
index tables are given on the following pages. 




Fig. 99. High Number Indexing Attachment 

For indexing prime, odd and even numbers. 



98 The Cincinnati Milling Machine Company 

Indexing. There are two methods of indexing employed: 

1. Plain Indexing. By converting the Head into plain index 
centers and using the front plate and index pin shown in the illus- 
trations. This plate has three circles of holes: 24, 30 and 36. 
It will index any number that divides evenly into any one of these. 
It is especially convenient for indexing low numbers, as when mak- 
ing four or six-fluted reamers, etc. It saves all the time lost by the 
old method of indexing through the side index plate, which requires 
ten turns of the pointer to make each one of the divisions of a four- 
fluted reamer. 

To change the Head from universal to direct indexing the worm 
is dropped out of mesh with the worm wheel by simply turning the 
T-bolt shown in Fig. 87 through half a turn. The indexing is done 
by turning the spindle by hand. When the job is finished the 
Head can be set for universal indexing again by turning the T-bolt 
in the opposite direction. All this can be done in a few seconds. 
The mechanism is positive in its action and does not depend upon 
clamping arrangements of any sort. 

2. Universal Indexing. This is the usual indexing arrange- 
ment by means of a plate and pin on the side of the head, but differs 
widely from others in the following very important feature: The 

PLATE IS PLACED CONCENTRIC WITH THE SWIVEL BLOCK, bringing 

it on a line with the work spindle, which enables us to use an index 
plate very much larger (8yf " in diameter) than is practical by any 
other construction. 

We employ only one plate. It is drilled on both sides, and 
reversible, and makes an unusually large number of useful divisions 
because its large diameter gives room for many circles and a large 
number of holes in these circles, and consequently a wider range of 
indexing than can be done from plates of smaller diameter. They 
include all numbers up to and including 60, and all even numbers 
and those divisible by 5 up to and including 120. 

The table furnished with the machine gives all divisions obtain- 
able up to 400. This covers the requirements of most shops. It 
is printed in full on page 76. 

If higher and prime numbers are to be indexed, the range of the 
index mechanism can be greatly extended by using the high number 
indexing attachment shown in Fig. 99. By using it, all indexing 
becomes simple indexing — no compound arrangement is necessary — 
no combinations of change gears need be set up to accomplish the 



A Treatise on Milling and Milling Machines 99 



result — there is no complicated and bothersome chart to be con- 
sulted. All obtainable divisions are indexed direct from the plates. 
This can be applied to any of our Dividing Heads, Combination 
Index Heads and 10" Plain Centers, and will index all numbers up 
to and including 200, all even numbers and those divisible by 5 up 
to and including 400, and make many divisions beyond. It may 
be added at any time at small cost. The complete high number 
indexing tables are printed on pages 103 and 104. 

How to Calculate Indexing. The calculations by which the 
index tables are produced and which must be followed for determin- 
ing the circle and moves for indexing numbers not given in the tables 
can, perhaps, be best understood by taking several practical examples 
which follow: 

First case: Indexing less than 40 divisions. Let us assume 
that a piece of work mounted between centers is to be divided into 
20 equal parts. This will require tV of a turn of the spindle for 
each division, and since the ratio between worm and wormwheel 
is 40 to 1, this will require to or two turns of the worm and, there- 
fore, two turns of the index crank. (The gears connecting the 
wormshaft and the index crankshaft are equal in size.) 

Second case: Indexing more than 40 divisions. Let us 
assume that it is desired to divide the circle into 80 divisions. 
This time the wormwheel will make sV of a turn, while the worm 
and index crank will make to or Yi a turn. In both of the above 
cases the index pointer always engages the same hole in the index 
plate, consequently it is immaterial which one of the even number 
circles of holes it is set to. 

Third case: Indexing 152 divisions. We have seen from the 
above two cases that, since the ratio between worm and worm- 
wheel is 40 to 1, 

(Rule 1.) Forty divided by the number of divisions required 
will determine the number of turns or the fractional part of a turn 
to be made by index pointer, which we saw was two turns for 20 
divisions and Yi a turn for 80 divisions. Now, following this rule, 
we will divide 40 by 152, which, expressed in the form of a fraction, 
is i 4 o D T, of which 

(Rule 2.) The denominator represents the circle to be used and 
the numerator represents the number of holes in this circle over 
which the index pin must be passed for each division. 



100 The Cincinnati Milling Machine Company 

Applying these rules to the first case mentioned we have the 
fraction ft, which we need analyze no further than to say that, if 
the pin were in the 20-hole circle, it would pass over 40 holes, or 
two turns for each division. Now, referring to our present case, we 
find that the index plate does not have a circle containing 152 holes. 
It is therefore necessary to transform this fraction into an equivalent 
fraction whose denominator will be the same number as the number 
of holes in one of the circles of the index plate. It does contain a 
38-hole circle. We will then transform our fraction iVt to the equiva- 
lent fraction of if, by dividing both the numerator and denominator 
by 4. Applying Rule 2 to this new fraction, 38 is the circle to which 
the index pin must be adjusted, and it must move over a series of 
10 holes for each one of the 152 divisions into which we are dividing 
our work. 

Fourth case: Indexing 33 divisions. Our fraction now takes 
the form of iHr. The plate does not contain a 33-hole circle, neither 
does it contain an 11-hole circle nor a 3-hole circle, and since 
these are the only numbers which can be evenly divided into 33, 
we must make our transformation by multiplying instead of divid- 
ing. We find that the plate does contain a 66-hole circle; there- 
fore, by transforming our fraction into an equivalent fraction of 
larger numbers by multiplying both numerator and denominator 
by 2, we get the equivalent fraction of It, in which 66 is the circle 
and 80 is the number of holes over which the pin must pass for each 
division; but since 80 holes are more than the 66-hole circle contains, 
we divide 80 by 66, and find that it is contained once with 14 left 
over; therefore, the pointer must make one complete turn and 14 
holes in addition. 

Fifth case: Indexing 395 divisions. Our fraction is i%=^« 
= tV, in which case we use the 79-hole circle and index over eight 
holes. 

The highest number that can be obtained with a High Number 
Indexing Attachment is 7960. Our fraction is two = rb. Here 
we must use the 199-hole circle and index one hole for each of the 
7960 divisions. 

The Sector. Referring to third case 'page 99): In order to 
save counting the ten holes each time, the index plate is provided 
with a sector, as shown in Fig. 100. The arms of this sector may be 
set by loosening the screw A so as to take between them any 
desired number of holes. One arm rests against the index pin. as 



A Treatise on Milling and Milling Machines 101 



indicated by the black hole, and the other arm is set 10 holes ahead. 
We must remember that the hole in which the pin rests must never 
be counted, for the simple reason that we are actually counting 
spaces and not holes. When the first division has bean made the 
index pin is moved forward 10 holes to the arm C of the sector, 

and the sector itself is 
moved up until the arm B 
again strikes the index pin. 
This will set arm C ahead 
the required distance to in- 
dicate the hole into which 
the index pin is to drop for 
the next division. In mov- 
ing the index pin forward it 
is always best to move slow- 
ly as the hole is approached 
and let the pin drop into 
place just as the hole is 
reached. In this way all 
the lost motion in the gear- 
ing is taken up. It will 
never do to let the pin pass 
the hole and then bring it 
back, because in this way 
the lost motion is not taken 
up and the indexing will not be accurate. Should the pin pass the 
hole accidentally, it must be brought back some distance and then 
moved forward again in the original direction and carefully placed 
in the hole. 




Example 152 Teeth 
5&C/rcle /O Holes 



Fig. 100 



Resetting Work to the Cutter 
Index Plate 



Notched 



It often occurs in toolmaking and experimental work that a piece 
of indexed work that has been milled must be put back into the 
machine for remilling. A simple case is that of a disk with teeth of 
some form on its periphery. If it is found that the teeth are all too 
thick, another cut must be taken all around the disk. 

When the work has been replaced in the machine, as before, it 
must be revolved the proper amount to bring the spaces to the cutter 
for recutting. This can not be done by indexing, because it will be 
found that when the work is in proper relation with the cutter, the 



102 



The Cincinnati Milling Machine Company 



index pin is somewhere between the holes. To meet this condition 
our index plate has notches in its periphery and the lock has cor- 
responding notches, Fig. 101. By loosening the lock and holding the 
index pinholder stationary, the plate can be revolved until one of 
the holes comes to the pin. The plate may then be locked again, 
the lock engaging a different set of notches. 

Again, it may be desired to remill indexed slots in order to cut 
them deeper. The problem now is to reset the work so the cutter 
will line up with the slots as originally cut. Here again, the final 
adjustment may be made by revolving the plate as in the previous 
case. Another very useful application of this feature is bevel or 
mitre gear cutting. When the blank is revolved toward the cutter, 
after the offset has been made, the index pin will nearly always 
fall between two holes. Then by revolving the plate we can bring 
one of the holes to the pin. 

The notches are of such size that by revolving the plate the 
amount of one notch, a piece of work 1" in diameter will be revolved 
.00017". The diameter of any piece of work multiplied by this 
figure gives the amount its periphery will be revolved (that is, the 
amount it will move towards the cutter). For example, a piece of 
work 6" diameter held between centers will be revolved toward the 
cutter 6 x . 00017" = .00102" for each notch that the index plate is 
revolved. This has proven a very useful feature on Cincinnati 
Dividing Heads. 




Fig. 101 

A section of the 8jf' diameter index plate showing the notches and lock. 



A Treatise on Milling and Milling Machines L03 



HIGH NUMBER INDEX TABLE 
For Simple Indexing High Numbers, Prime, Odd and Even 

FOR USE WITH HIGH NUMBER INDEXING ATTACHMENT. 
INDEXES ALL NUMBERS UP TO AND INCLUDING 200; ALL EVEN 
NUMBERS AND THOSE DIVISIBLE BY 5 UP TO AND INCLUDING 4OO, 
EXCEPT 225-275-325-375. 

This attachment consists of a set of 3 index plates which are 
drilled on six sides, A, B, C, D, E and F. (See note, page 106.) 

Example to index 35 divisions: The preferred side is F, since this 
requires the least number of holes. But should either D, A or E be 
in place, it can be used, thus avoiding the bother of changing plates. 



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104 



The Cincinnati Milling Machine Company 



Index Table for High Numbers — Continued 



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41 


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123 


120 


66 


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99 


60 


92 


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69 


30 


42 


E 


42 


-\ 


67 


B 


67 


40 


92 


E 


161 


70 


42 


A 


147 


140 


68 


C 


34 


20 


93 


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40 


43 


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129 


120 


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70 


94 


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141 


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187 


110 


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A 


171 


72 


45 


B 


36 


32 


70 


D 


42 


24 


96 


B 


36 


15 


45 


A 


99 


SS 


70 


A 


91 


52 


96 


A 


48 


20 


45 


C 


153 


136 


70 


E 


119 


65 


97 


B 


97 


40 


46 


C 


46 


40 


71 


F 


71 


40 


98 


A 


:,7 


60 


46 


A 


69 


oO 


72 


B 


36 


20 


99 


A 


99 


40 


46 


E 


161 


140 


72 


A 


117 


6-5 


100 


A 


30 


12 


47 


B 


141 


120 


72 


C 


153 


55 


100 


E 


175 


70 


48 


A 


30 


25 


73 


E 


" 


#0 


101 


F 


101 


40 


48 


B 


36 


;: 


74 


B 


Ill 


60 


102 


C 


153 


60 


49 


A 


147 


120 


75 


A 


30 


- ,: ; 


103 


E 


103 


40 


50 


A 


30 


24 


76 


F 


35 


20 


104 


E 


26 


10 


50 


E 


175 


140 


76 


E 


133 


70 


104 


A 


91 


35 


51 


C 


:5o 


120 


76 


A 


171 


-' 


104 


F 


143 


55 


52 


E 


26 


at 


77 


D 


-- 


40 


104 


B 


169 


6-5 


52 


A 


91 


70 


78 


A 


117 


60 


105 


E 


42 


16 


52 


F 


143 


110 


79 


c 


79 


40 


105 


A 


147 


56 


52 


B 


: '■ 


130 


80 


E 


- 


13 


106 


F 


159 


60 


53 


F 


159 


120 


80 


F 


2- 


14 


107 


D 


107 


40 


54 


B 


81 


60 


80 


A 


30 


15 


108 


B 


81 


30 


54 


A 


189 


140 


80 


D 


32 


16 


108 


A 


:>9 


70 


DO 


D 


44 


.-_ 


80 


C 


34 


17 


109 


c 


109 


40 


55 


F 


143 


104 


80 


B 


36 


18 


110 


D 


4. 


16 


56 


F 


28 


20 


80 


E 


42 


21 


110 


A 


99 


36 


56 


E 


42 


30 


81 


B 


81 


40 


110 


F 


143 


52 


56 


D 


77 


55 


82 


c 


123 


60 


111 


B 


111 


40 


56 


A 


91 


65 


83 


F 


83 


40 


112 


F 


28 


10 


57 


A 


171 


:_: 


84 


E 


42 


20 


112 


E 


42 


15 


58 


E 


87 


IV J 


84 


A 


147 


70 


113 


F 


113 


40' 


59 


A 


177 


120 


85 


C 


34 


10 


114 


A 


171 


60 


60 


A 


30 


20 


85 


E 


119 


•56 


115 


C 


46 


16 


60 


B 


36 


2 4 


85 


F 


157 


- 


115 


A 


69 


24 


60 


E 


42 


' ' -v 


86 


A 


129 


60 


115 


E 


161 


56 


60 


F 


159 


:06 


87 


E 


87 


40 


116 


E 


n 


30 


61 


B 


183 


120 


88 


D 


44 


20 


117 


A 


117 


40 


62 


C 


93 


60 


88 


A 


99 


45 


118 


A 


177 




63 


A 


159 


120 


88 


F 


143 


65 


119 


E 


119 


40 


64 


D 


32 


Ot~| 


89 


D 


59 


40 


120 


A 


30 


10 


64 


A 


4> 


3 j 


90 


B 


36 


16 


120 


B 


36 


12 


65 


E 


26 


It) 


90 


A 


99 


44 


120 


E 


42 


14 


65 


A 


91 


56 


90 


C 


153 


6^ 


120 


C 


93 


31 


65 


F 


143 


55 


91 


A 


91 


4«:i 


120 


F 


159 


53 


65 


B 


169 


104 


92 


c 


46 


: 


121 


D 


121 


40 



A Treatise on Milling and Milling Machines 105 



Index Table for High Numbers — Continued 



09 








a 








» 








a 








c 








c 








_c 


































°3! 








V) 








> 

3 


-c 


Ih 


IA 

c 


5 


i> 


V 

u 

u 


IB 

u 

c 


> 

5 


u 


u 
u 


u 




C 


5a 


U 


X 





'in 


U 


X 


O 


c/5 


(3 


X 




















d 








£ 








z 








fe 








122 


B 


183 


60 


160 


F 


28 


7 


197 


C 


197 


40 


123 


C 


123 


40 


160 


D 


32 


8 


198 


A 


99 


20 


124 


C 


93 


30 


160 


B 


36 


9 


199 


B 


199 


40 


125 


E 


175 


56 


160 


A 


48 


12 


200 


A 


30 


6 


126 


A 


189 


60 


161 


E 


161 


40 


200 


E 


175 


35 


127 


B 


127 


40 


162 


B 


81 


20 


202 


F 


101 


20 


128 


D 


32 


10 


163 


D 


163 


40 


204 


C 


153 


30 


128 


A 


48 


15 


164 


C 


123 


30 


205 


C 


123 


24 


129 


A 


129 


40 


165 


A 


99 


24 


206 


E 


103 


20 


130 


E 


26 


8 


166 


F 


83 


20 


208 


E 


26 


5 


130 


A 


91 


28 


167 


C 


167 


40 


210 


E 


42 


8 


130 


F 


143 


44 


168 


E 


42 


10 


210 


A 


147 


28 


130 


B 


169 


52 


168 


A 


147 


35 


212 


F 


159 


30 


131 


F 


131 


40 


169 


B 


169 


40 


214 


D 


107 


20 


132 


A 


99 


30 


170 


C 


34 


8 


215 


A 


129 


24 


133 


E 


133 


40 


170 


E 


119 


28 


216 


B 


81 


15 


134 


B 


67 


20 


170 


F 


187 


44 


216 


A 


189 


35 


135 


B 


81 


24 


171 


A 


171 


40 


218 


C 


109 


20 


135 


A 


189 


56 


172 


A 


129 


30 


220 


1) 


44 


8 


136 


C 


34 


10 


173 


F 


173 


40 


220 


A 


99 


18 


136 


E 


119 


35 


174 


E 


87 


20 


220 


F 


143 


26 


137 


D 


137 


40 


175 


E 


175 


40 


222 


B 


111 


20 


138 


A 


69 


20 


176 


D 


44 


10 


224 


F 


28 


5 


139 


C 


139 


40 


177 


A 


177 


40 


226 


F 


113 


20 


140 


F 


28 


8 


178 


D 


89 


20 


228 


A 


171 


30 


140 


E 


42 


12 


179 


D 


179 


40 


230 


C 


46 


8 


140 


D 


77 


22 


180 


B 


36 


8 


230 


A 


69 


12 


140 


A 


91 


26 


180 


A 


99 


22 


230 


E 


161 


28 


141 


B 


141 


40 


180 


C 


153 


34 


232 


E 


87 


15 


142 


F 


71 


20 


181 


C 


181 


40 


234 


A 


117 


20 


143 


F 


143 


40 


182 


A 


91 


20 


235 


B 


141 


24 


144 


B 


36 


10 


183 


B 


183 


40 


236 


A 


177 


30 


145 


E 


87 


24 


184 


C 


46 


10 


238 


E 


119 


20 


146 


E 


73 


20 


184 


A 


69 


15 


240 


A 


30 


5 


147 


A 


147 


40 


184 


E 


161 


35 


240 


B 


36 


6 


148 


B 


111 


30 


185 


B 


111 


24 


240 


E 


42 


7 


149 


E 


149 


40 


186 


C 


93 


20 


240 


A 


48 


8 


150 


A 


30 


8 


187 


F 


187 


40 


242 


D 


121 


20 


151 


D 


151 


40 


188 


B 


141 


30 


244 


B 


183 


30 


152 


F 


38 


10 


189 


A 


189 


40 


245 


A 


147 


24 


152 


E 


133 


35 


190 


F 


38 


8 


246 


C 


123 


20 


152 


A 


171 


45 


190 


E 


133 


28 


248 


c 


93 


15 


153 


C 


153 


40 


190 


A 


171 


36 


250 


E 


175 


28 


154 


D 


77 


20 


191 


E 


191 


40 


252 


A 


189 


30 


155 


C 


93 


24 


192 


A 


48 


10 


254 


B 


127 


20 


156 


A 


117 


30 


193 


r> 


193 


40 


255 


C 


153 


24 


157 


B 


157 


40 


194 


B 


97 


20 


256 


D 


32 


5 


158 


C 


79 


20 


195 


A 


117 


24 


258 


A 


129 


20 


159 


F 


159 


40 


196 


A 


147 


30 


260 


E 


26 


4 



106 



The Cincinnati Milling Machine Company 



Index Table for High Numbers — Continued 



■f. 

a 

_c 
'7. 
> 

5 

c 


a 

2 
in 


u 

u 

O 


m 




■j-. 

c 
_c 
'7. 
"> 

5 

c 




■■j 
o 


■s. 

V 

c 
X 


of Divisions 


u 

33 


_a 

u 


a 


d 








c 








c 








260 


A 


91 


14 


305 


B 


183 


24 


355 


F 


71 


8 


260 


F 


143 


22 


306 


C 


153 


20 


356 


D 


89 


10 


260 


B 


169 


26 


308 


D 


77 


10 


358 


D 


179 


20 


262 


F 


131 


20 


310 


C 


93 


12 


360 


B 


36 


4 


264 


A 


99 


15 


312 


A 


117 


15 


360 


A 


99 


11 


265 


F 


159 


24 


314 


B 


157 


20 


360 


C 


153 


17 


266 


E 


133 


20 


315 


A 


189 


24 


362 


C 


181 


20 


268 


B 


67 


10 


316 


C 


79 


10 


364 


A 


91 


10 


270 


B 


81 


12 


318 


F 


159 


20 


365 


E 


73 


8 


270 


A 


189 


28 


320 


D 


32 


4 


366 


B 


183 


20 


272 


C 


34 


5 


320 


A 


48 


6 


368 


C 


46 


5 


274 


D 


137 


20 


322 


E 


161 


20 


370 


B 


111 


12 


276 


A 


69 


10 


324 


B 


81 


10 


372 


C 


93 


10 


278 


C 


139 


20 


326 


D 


163 


20 


374 


F 


187 


20 


280 


F 


28 


4 


328 


C 


123 


15 


376 


B 


141 


15 


280 


E 


42 


6 


330 


A 


99 


12 


378 


A 


189 


20 


280 


D 


77 


11 


332 


F 


83 


10 


380 


F 


38 


4 


280 


A 


91 


13 


334 


C 


167 


20 


380 


E 


133 


14 


282 


B 


141 


20 


335 


B 


67 


8 


380 


A 


171 


18 


284 


F 


71 


10 


336 


E 


12 


5 


382 


E 


191 


20 


285 


A 


171 


24 


338 


B 


169 


20 


384 


A 


48 


5 


286 


F 


143 


20 


340 


C 


34 


4 


385 


D 


77 


8 


288 


B 


36 


5 


340 


E 


119 


14 


386 


D 


193 


20 


290 


E 


87 


12 


340 


F 


187 


22 


388 


B 


97 


10 


292 


E 


73 


10 


342 


A 


171 


20 


390 


A 


117 


12 


294 


A 


147 


20 


344 


A 


129 


15 


392 


A 


147 


15 


295 


A 


177 


24 


345 


A 


69 


8 


394 


C 


197 


20 


296 


B 


111 


15 


346 


F 


173 


20 


395 


C 


79 


8 


298 


E 


149 


20 


348 


E 


87 


10 


396 


A 


99 


10 


300 


A 


30 


4 


350 


E 


175 


20 


398 


B 


199 


20 


302 


D 


151 


20 


352 


D 


44 


5 


400 


A 


30 


3 


304 


F 


38 


5 


354 


A 


177 


20 











Note. — These three plates have holes as follows: 

v /A— 30, 48, 69, 91, 99, 117, 129. 147, 171, 177, 189 

±-late j B _ 36> 67> 81j 97j m 12 7 ? ui, 157, 169, 183, 199 

^ /C— 34, 46, 79, 93, 109, 123, 139, 153, 167, 181, 197 

^late <^ D _ 32) 44 } 77j 89> 107, 121, 137, 151, 163, 179, 193 

v /E— 26, 42, 73, 87, 103, 119, 133, 149, 161, 175, 191 

±-late ^ F _ 28} 38) 7i> 83> ioi, 1L3, 131, 143, 159, 173, 187 



A Treatise on Milling and Milling Machines 107 



STANDARD INDEX TABLE 
For the Standard Index Plate Used with Dividing Head 

INDEXES AIL NUMBERS UP TO AND INCLUDING 60; ALL EVEN NUMBERS AND 
THOSE DIVISIBLE BY 5 UP TO 120, AND ALL DIVISIONS OBTAINABLE UP TO 4OO. 

This Plate is drilled on both sides and has holes as follows: 

FIRST SI DE — 24-25-28-30-34-37-38-39-41-42-43. 
SECOND SIDE— 46-47-49-51-53-54-57-58-59-62-66. 



W 




1 




</) 






en 






(/> 






C 








a 






C 






C 






O 















O 













"35 








"3! 






"3 






"3 






°> 


32 


w 


(A 


*rj 


U 


in 


'> 


z> 


(0 


"^ 


u 


!/> 


5 


"u 


c 





5 


73 

u 


O 


s 


"3 


U 




5 


"2 








O 


h 


a 


Cm 

O 


'6 


a 


<4- 




6 


K 


O 


c 


X 


0* 








d 






d 






d 






z 








ft 






55 






fe 






2 


ANY 


20 




44 


66 


60 


104 


39 


15 


205 


41 


8 


3 


24 


13 


's 


45 


54 


48 


105 


42 


16 


210 


42 


8 


4 


ANY 


10 




46 


46 


40 


106 


53 


20 


212 


53 


10 


5 


ANY 


8 




47 


47 


40 


108 


54 


20 


215 


43 


8 


6 


24 


6 


±6 


48 


24 


20 


110 


66 


24 


216 


54 


10 


7 


28 


5 


20 


49 


49 


40 


112 


28 


10 


220 


66 


12 


8 


ANY 


5 




50 


25 


20 


114 


57 


20 


224 


28 


5 


9 


54 


4 


24 


51 


51 


40 


115 


46 


16 


228 


57 


10 


10 


ANY 


4 


# # 


52 


39 


30 


116 


58 


20 


230 


46 


8 


11 


66 


3 


42 


53 


53 


40 


118 


59 


20 


232 


58 


10 


12 


24 


3 


8 


54 


54 


40 


120 


66 


22 


235 


1 47 


8 


13 


39 


3 


3 


55 


66 


48 


124 


62 


20 


236 


59 


10 


14 


49 


2 


42 


56 


28 


20 


125 


25 


8 


240 


66 


11 


15 


24 


2 


16 


57 


57 


40 


130 


39 


12 


245 


49 


8 


16 


24 


2 


12 


58 


58 


40 


132 


66 


20 


248 


62 


10 


17 


34 


2 


12 


59 


59 


40 


135 


54 


16 


250 


25 


4 


18 


54 


2 


12 


60 


42 


28 


136 


34 


10 


255 


51 


8 


19 


38 


2 


4 


62 


62 


40 


140 


28 


8 


260 


39 


6 


20 


ANY 







64 


24 


15 


144 


54 


15 


264 


66 


10 


21 


42 




38 


65 


39 


24 


145 


58 


16 


270 


54 


8 


22 


66 




54 


66 


66 


40 


148 


37 


10 


272 


34 


5 


23 


46 




34 


68 


34 


20 


150 


30 


8 


280 


28 


4 


24 


24 




16 


70 


28 


16 


152 


38 


10 


290 


58 


8 


25 


25 




15 


72 


54 


30 


155 


62 


16 


296 


37 


5 


26 


39 




21 


74 


37 


20 


156 


39 


10 


300 


30 


4 


27 


54 




26 


75 


30 


16 


160 


28 


7 


304 


38 


5 


28 


42 




18 


76 


38 


20 


164 


41 


10 


310 


62 


8 


29 


58 




22 


78 


39 


20 


165 


66 


16 


312 


39 


5 


30 


24 




8 


80 


34 


17 


168 


42 


10 


320 


24 


3 


31 


62 




18 


82 


41 


20 


170 


34 


8 


328 


41 


5 


32 


28 




7 


84 


42 


20 


172 


43 


10 


330 


66 


8 


33 


66 




14 


85 


34 


16 


176 


66 


15 


336 


42 


5 


34 


34 




6 


86 


43 


20 


180 


54 


12 


340 


34 


4 


35 


28 




4 


88 


66 


30 


184 


46 


10 


344 


43 


5 


36 


54 




6 


90 


54 


24 


185 


37 


8 


360 


54 


6 


37 


37 




3 


92 


46 


20 


188 


47 


10 


368 


46 


5 


38 


38 




2 


94 


47 


20 


190 


38 


8 


370 


37 


4 


39 


39 




1 


95 


38 


16 


192 


24 


5 


376 


47 


5 


40 


ANY 






96 


24 


10 


195 


39 


8 


380 


38 


4 


41 


41 1 


. . 


40 


98 


49 


20 


196 


49 


10 


390 


39 


4 


42 


42 


, . 


40 


100 


25 


10 


200 


30 


6 


392 


49 


5 


43 


43 I 




40 


102 


51 


20 


204 


51 


10 


400 


30 


3 



108 The Cincinnati Milling Machine Company 



CHAPTER IV 
SETTING UP THE MACHINE 

Placing Cutters on the Arbor. When setting up the machine 
preparatory to milling a piece of work, care should be taken to have 
the cutters as close to the end of the spindle as the work will per- 
mit. Milling Machine arbors in general use are as a rule very much 
smaller in diameter than they should be, and their weakness is simply 
emphasized by placing cutters at or near the middle of a long, unsup- 
ported arbor. Cutters on hand may have small holes, making small 
diameter arbors necessary, but whenever new cutters are ordered, 
careful consideration should be given to having them made large 
enough to permit of using arbors of large diameter, since it is only 
with properly designed cutters and arbors of sufficient size that the 
best results can be obtained from modern High-Power Milling 
Machines. (See paragraph on chattering, page 118.) 

Cutters should always be keyed to the arbors. The friction due 
to tightening up the arbor nut can not be expected to hold them. 
Particular attention should be paid to the proper cleansing of the 
hole in the spindle and the taper shank of the arbor. Unless this 
point is carefully watched, a true running arbor can not result, 
accurate work can not be secured, both the hole in the spindle and 
the bush in the arbor support will be spoiled. The body of the arbor, 
the arbor collars, and the shank should be thoroughly cleaned before 
the cutters and collars are placed on the arbor. Any foreign matter 
between these members will bend the arbor when the nut is tightened. 

Arbor Supports. We supply with all our machines two differ- 
ent styles of arbor supports. For the small arbors which have a 
bearing on the outside of the arbor nut, there is a suitable adjust- 
able bronze bush in one of the supports. The larger arbors all 
have one or two spacing collars that are larger than the rest, and 
these collars fit the bushing in the arbor bearing bracket and serve 
to give the arbor an additional support. This bearing collar should 
be as close to the cutters as practical so that the support may be 
close to the cutters and thus properly support the arbor. The 



A Treatise on Milling and Milling Machines 109 



braces for tying the arbor support to the knee of the machine should 
always be used if the work will permit. 



SPIMOLEj-i 




Fig. 102 

Fig. 102. All short arbors are provided with a pilot bearing at 
the end. This fits a split bronze bushing, X, in the arbor support. 
Adjust this bushing to a close bearing. 

Spihole. „ 







J" l» 

Y 




Fig. 103 

Fig. 103. Some medium length arbors have in addition to an 
end pilot bearing, X, as above, an arbor bearing collar to fit the 
intermediate support Y. This support should be placed as close 
to the cutter as practical, the cutter itself being located as close 
to the shoulder of the arbor as conditions will permit. 



5PINQLE 




Fig. 104 



Fig. 104. Another style of medium length arbor does not have 
the pilot bearing for bronze bush at end, but is furnished with a 
bearing collar which permits of placing the support anywhere 
close to the cutter. 







mi 



^p 



/ 

BRBCtS 



Fig. 105 



Fig. 105. All our long arbors have two bearing collars. When- 
ever possible, one of these, Y, should be placed between cutters 
that are spaced some distance apart on the arbor and the other, 
Z, to which the braces are fastened, should be as close to the out- 
side of the gang as conditions will permit. 



110 



The Cincinnati Milling Machine Company 




Fig. 106 

Fig. 106. Another way of supporting a long arbor. In this case 
the width of the table does not permit of bringing the support Z, 
to which the braces are fastened, close to the cutters. The inter- 
mediate support Y is therefore placed close to the gang and 
between it and the outer support Z. 




Fig. 107 



Fig. 107. Sometimes the nature of the work requires the cutters 
to be near the outer end of the arbor. Then the intermediate 
support Y should be placed inside of the gang, that is, between the 
gang and the spindle. 



SPirsoLE. 




n 




y 



kcz 



Fig. 108 



5=* = C = 5 



Fig. 108. The Wrong Way. In all of the above cases the cut- 
ters have been placed as near the end of the spindle as conditions 
permit. When this was not possible the supports have been placed 
close to each side of the cutters. Compare these conditions with 
this sketch, which shows a cutter in the middle of a long, unsupported 
arbor. This sort of set-up should never be tolerated. It can not 
possibly produce satisfactory results. 



A Treatise on Milling and Milling Machines 111 



The Drive for Arbors and Cutters. All of our High Power 
Machines as well as our larger Cone Driven Machines, Automatic 




Fig. 109 



Machines and Manufacturing Machines have flanged spindles, 
as shown in Fig. 109. These flanges are fitted with hardened keys. 




■%-MTHS.U.S.S 
H FULLDEPTH OF THREAD 
Fig. 110 



112 



The Cincinnati Milling Machine Company 



The cutter arbors are made of solid forgings providing corresponding 
flanges for driving. This provides a powerful, durable drive that is 
not easily injured even when doing the heaviest cutting. Face 
mills are driven in the same way. They are slightly counterbored 
to fit over the flanges, thus centering them, and they are recessed 
to receive the driving keys. They are held in place by four screws. 





SECTION C-C 



SECTION R-fl 



No.l CONE-TYPE 


2l6 


2-8THS.-U.S.S. 


HoZ " " 


2,6 


2.-8-THS.-U.9S. 


No.3 " " 


2% 


2i-6THS.-U.55. 


NO.2 HIGH-POWER 


Zh 


2 z.- -t P.- 5 -ThS.-U.SS- 1.250 LE HD- 






| Spirhl RNGLE 3°4o° 



NO. 3 STD. HIGH POWER 




.999 



Section b-b 




Section d-d 



No4 high power 

No4 CONE HIGH POWER 


4ia 


4 -4 P. - 5 THS.- US.S .- 2 LER D 
SPlRHL RNGUE 9°40' 


No 5 high Power 


4# 2 


4^-4 P.-5THS.-U.S.S.-2LeR0 
SPlRRL RNGLE 9"4' 



NO. 3 HIGH POWER 
NO. 4 STD. HIGH POWER 



Fig. Ill 

This is simpler than the use of threaded spindle ends; it makes a 
more powerful drive, and mills are easily removed after doing heavy 
cutting. 

The same face mill will fit all sizes and styles of Cincinnati 
Millers which have flanged spindle ends. This complete interchange- 
ability reduces the number of face mills it is necessary to keep on 
hand. Complete working dimensions for use when making face 



A Treatise on Milling and Milling Machines 113 

mills to fit standard flanged spindle ends are given in the drawing 
Fig. 110. 

Spindle Flanges for Threaded Spindles. It will be found 
very simple to put flanges on the older machines having threaded 
spindle ends, and thus gain the full advantage of complete inter- 
changeability of face mills between these and the later machines. 
On some sizes such a flange will also adapt the older machine for 
using the new flanged arbors. 

The sketches, Fig. Ill, show flanges suitable for Cincinnati 
Millers with threaded spindles as made in recent years, and give 
sufficient dimensions to enable anyone to make similar flanges to 
suit the spindle ends of any other Cincinnati machines. 

Cutter Arbors. All our arbors 1" diameter and larger have 
standard keyways as listed in the table. These are also the standard 
key ways used in cutters. 

Standard Keyways for Cutters and Arbors 




Fig. 112 



Diameter of Hole (D) 


Width (W), 


Depth (A), 


Radius (E), 


in Cutter, Inches 


Inches 


Inches 


Inches 


Hto A 


3 
32 


3 
64 


.020 


5 Ato y 8 


Vs 


i 

16 


.030 


Htoifc 


A 


5 

61 


.035 


1 A to 1% 


3 
16 


3 

32 


.040 


l^tol^ 


H 


Vs 


.050 


lif to 2 


5 

16 


s 

32 


.060 


2^ to 2V 2 


N 


3 
16 


.060 


2^ to 3 


7 
16 


3 
16 


.060 



Cutters should be held on the arbor by keys that are a good side 
fit in the keyways in both the cutter and the arbor. The height of 
the key should be a little less than twice A, so as to have top 
clearance. A key that fits top and bottom like a wedge and not 
on the sides is bad because it will roll and ruin the arbor, and prob- 
ably split the cutter in two. 



114 



The Cincinnati Milling Machine Company 



When heavy cutting is done, there is always the danger that the 
side pressure will cause the key even when properly fitted, to crush 
in the side of the keyway in the arbor. It is best to make the key 
longer than the cutter. This is especially true of narrow cutters such 
as saws. By using a long key the pressure is distributed over a 
greater area, reducing the tendency to crush the keyway. The 
better method of driving large narrow saws is through a flange 
fitted with pins which will drive through holes drilled in the saws. 

For especially heavy service, the special key and keyway, Fig. 
113, was designed, the idea being to substitute for the shearing 
action of the ordinary key, a wedging action that would have no 
tendency to distort either key or arbor. The arbor is first flattened 
and then a standard size keyway is milled into it. 

The keyway in the cutter is an arc of a circle and the key is 
made out of a piece of round stock milled in on both sides and then 
sawed apart lengthwise, one piece of stock forming two keys. 

If, for instance, the driving pressure is from right to left, the 
key will be forced over to the right and the flat portion of the key 
pressed down on the flat on the left of the arbor. This pressure 
being almost directly downward, there is practically no side pressure, 
and therefore no distortion of the keyway in the arbor can result. 

This style of key has proven very satisfactory. Cutters so 
mounted can be readily removed after the heaviest milling. 




RRBOR 



,HOLE IN CUTTER - 
Fig. 113 



.9737 
1.0378 
1.2187 
1.4543 
1.7111 
1.9473 



B 


c 


5 


5 


32 


64 


5 


5 


32 


64 


3 


3 


16 


32 


M 


Vs 


M 


Vs 


5 


5 


16 


32 



D 



1 

m 

2 



E 



1.0518 
1.1159 
1.3125 
1.5793 
1.8361 
2.1036 



5 
32 

5 
32 

3 
16 

X 
H 



G 



32 

Vs 



5 
32 



H 



13 
64 
13 
64 

X 

21 
64 
21 
64 
13 
32 



.0263 
.0247 
0312 
0457 
.0389 
0527 



A Treatise on Milling and Milling Machines 115 



Arbor Equipments for Millers are as Follows: 



Machine 
Size 



Arbor Included 



Arbor Sent on 
Approval 



Gone-Type Machines 



IS" PI. 
IS" B. 


G. 


IS" PI. 


Mfg. 


1 PI. 




2 PI. 




3 PI. 




4 PI. 




1 Un. 
2Un. 
3Un. 
4Un 





No. 11—1" x 8" 
No. 11—1" x 8" 
No. 16—1" x 10" 
No. 91— 14" x 12" 



No. 09- 
No. 09- 
f No. 141- 
l No. 143- 
No. 11- 
No. 41- 
No. 11- 
No. 43- 
No. 81- 
No. 86- 
No. 92- 
No. 103- 



-1" x 

-1" x 

-1" x 
"14" x 

-1" x 

-1" X 

-1" X 

-14" x 
-14" x 

-W x 

-1V 2 " x 
-2" x 



6" 

6" 

143^" 

14^" 

8" 

14M" 
8" 

UVo" 
12" 
29" 
14" 
36" 



No. 

No. 
No. 


43- 

86- 

103- 


-14" 
-iy 2 " 

-2" 


x uy 2 " 

x29" 
x36" 



M Type Constant Speed Drive Machines 

With Flanged Spindle Ends 



IM PI. 




{ No. 112—1" x 8" 

{ No. 118—14" x 20" 

No. 118—14" x 20" 

No. 118— 14" x 20" 


2AI PI. 




IM Un. 
2M Un. 


No. 112— l"x8" 
No. 112—1" x 8" 



High -Power Machines 

Constant Speed Drive with Flanged Spindle Ends 





2 PI. 






No. 
No. 


16- 

86- 


-1" 

-lA" 


x 10" 














x29" 




3 PI. 


Std. 












No. 
No. 


81—14" 
86— 1H" 


xl2" 














x29" 




3 PI. 














No. 
No. 


81- 

86- 


-14" 
-IA" 


x 12" 














x29" 




4 PI. 


Std. 












No. 
No. 


81—14" 
86— W 


xl2" 














x29" 




4 PI. 














No. 


105- 


-Wo" 


x27" 


















No. 


110—2" 


x38" 




5 PL 














No. 


105- 


-1A" 


x27" 


















No. 


110- 


-2" 


x38" 




2Un. 




No. 


16—1 


x 


10" 


No. 


86—li^" 


x29" 




3Un. 


Std. 


No. 


16- 


-1" 


x 


10" 


No. 


86- 


-IV?!' 


x29" 




3Un. 




No. 


16- 


-1" 


X 


10" 


No. 


86- 


-IV?!' 


x29" 




4Un. 


Std. 


No. 


16- 


-1" 


x 


10" 


No. 


86- 


-\A" 


x29" 




4Un. 




No. 


105- 


-VA" 


x 


27" 


No. 


110- 


-2" 


x38" 




5Un. 




No. 


105- 


-VA" 


X 


27" 


No. 


110—2" 


x38" 



116 



The Cincinnati Milling Machine Company 



3 s ■ 



wm**mmmmmmmmfi 



samMamOUm^msm 



STYLE A 



STYLE D 




mmamm 






f ' ' " 

= =2 -'- . 



iii 



STYLE C — Can be used only in spindles having threaded end STYLE B 

* i ) 




STYLE F — Can be used onlv in soindles having threaded end 




STL YE G — Can be used only in spindles having flanged end 




STYLE J — Can be used only in spindles having flanged end 
Arbors for Machines with THREADED Spindle Nose 



Any arbor between two cross 
lines will fit any machine 
between the same cross lines. 







No. 


No. 


Style 


of 

Taper 



Length Diameter 
from of 

Diameter Shoulder Bearing 

to Nut ' Collar 



No. 1 Plain or Universal Cone 



No. 2 Plain or Universal Cone 

No. 2 Plain or Universal High 
Power Threaded Spindle. . . . 



"10 


A 


10 


11 


A 


10 


13 


A 


10 


41 


D 


10 


43 


D 


10 


44 


D 


10 


45 


D 


10 



1 

IX 

1 

Wo 



8 
8 

14- 2 

uy 2 

27 
27 



No. 3 Plain or Universal Cone 
Threaded Spindle 



16 


A 


11 1 


18 


B 


11 


53 


D 


11 


55 


D 


11 


56 


D 


11 



1 
\y A 

i 



10 
10 

IS 1 * 
IS 1 9 
18U 



2 3 > 

2 3 s 
2H 



No. 3 Plain or Universal 
Standard 

No. 3 Plain or Univ. High 
Power Threaded Spindle. . . . | 



59 



Oi 



11 



11 






29 
29 



? 3 5 
23 i 



No. 4 Plain or Universal Cone 

No. 5 Plain or Universal Cone 
Threaded Spindle 



90 


A 


12 


25 


C 


12 


26 


C 


12 


66 


F 


12 


67 


F 


12 


69 


F 


12 



1 

m 

IV 2 

m 

9 



10 
12 

14 
26 
26 
26 



2*4 

2% 
2Vs 
2% 
2*4 



IS' Plain Cone 

18" Back Geared Cone. 



OS 
09 



A 
A 



1 



•When it is necessary to use a Jg' arbor on the larger machines we recommend this No. 10 arbor 
in connection with standard collets as follows: 

Nob. 2 and 3 High-Power, No. 3 Standard and Cone Type Machines with flanged or threaded 
spindle ends, use 459 collet. 

Nos. 4 and .5 Machines with threaded spindle ends, and No. 4 with flanged spindle ends, use 461 
collet. 

Nos. 4 and 5 Machines, with No. 14 taper hole, use 463 collet 



A Treatise on Milling and Milling Machines 117 



Arbors for Machines with FLANGED Spindle Nose 



Anv arbor between two cross 










Length 


Diam- 




lines will fit any machine 






Xo. of 


Diam- 


from 


eter of 




between the same cross 


Xo. 


Stvle 


Taper 


eter 


Shoulder 


Bearing 


Flanged 


lines 










to Nut 


Collar 






112 


A 


14 




8 






Xo. 1 M Plain or Universal . . 


118 


D 


14 


IX 


20 


2% 




Xo. 2 Plain or Universal 


tll9 


J 


14 




21 


2K 


Yes 




tl20 
16 


J 


14 


IK 


21 


2% 


Yes 


Xo. 2 PI. or Uni High Power 


A 


11 




10 






Xo. 3 Plain or Universal Cone 


81 


G 


11 


IK 


12 


2% 


Yes 


Xo. 3 Plain or Uni. Standard 


83 


J 


11 


IK 


18K 


2K 


Yes 


Xo. 3 PI. or Uni. High Power 


84 


J 


11 


m 


18K 


2% 


Yes 


Xo. 4 Plain or Universal 


85 


J 


11 


IK 


29 


2K 


Yes 


Standard Flanged Spindles 


86 
90 


J 


11 


V/i 


29 
10 


2K 


Yes 




A 


12 








91 


G 


12 


IK 


12 


2K 


Yes 


Xo. 4 Plain or Universal Cone 


92 


G 


12 


m 


14 


2K 


Yes 




93 


J 


12 


IK 


26 


2% 


Yes 


Xo. 4 Plain or FJ niversal High 


94 


J 


12 


Wo 


26 


2K 


Yes 


Power 


95 


J 


12 


IK 


26 


2% 


Yes 


Xo. 5 Plain or Universal High 


96 


J 


12 




26 


2% 


Yes 


Power 


101 


J 


12 


IK 


36 


m 


Yes 


Xo. 12 Taper. Flanged Spin- 


102 


J 


12 


IK 


36 


2% 


Yes 


dle 


103 
104 


J 
J 


12 




36 


2K 


Yes 


Xo. 4 Plain or Universal High 


14 


IK 


27 


• 2% 


Yes 


Power 


105 


J 


14 


IK 


27 


2% 


Yes 


Xo. 5 Plain or Universal High 


107 


J 


14 




27 


2% 


Yes 


Power Flanged Spindle .... 


108 


J 


14 


IK 


38 


2K 


Yes 


No. 14 Taper 


110 


J 


14 




38 


2K 


Yes 




111* 


J 


14 


2K 


38 


3K 


Yes 




41 


D 


10 




14K 


2 






43 


D 


10 


IK 


14K 


2 






fl41 


J 


10 




14K 


2 


Yes 


18" Plain Manufacturing. . . . 


|143 


J 


10 


IK 


14K 


2 


Yes 




16 


A 


11 




10 








18 


B 


11 


IK 


10 


2K 






53 


D 


11 




18K 


2% 




18" Automatic 


55 


D 


11 


IK 


18K 


2% 




24" Automatic 


56 
81 


D 


11 


IK 


18K 


2% 






G 


11 


IK 


12 


2% 


Yes 




83 


J 


11 


IK 


18K 


2% 


Yes . 




84 
104 


J 


11 


IK 


18K 


2K 


Yes 




J 


14 


IK 


27 


2K 


Yes 




105 


J 


14 


IK 


27 


2% 


Yes 


48" Automatic 


107 


J 


14 


2 


27 


2K 


Yes 




108 


J 


14 


IK 


38 


2% 


Yes 




110 


J 


14 


2 


38 


2K 


Yes 



tFurnished with only one bearing collar. 

*Arbor No. Ill includes special bushing for arbor supports. 



118 The Cincinnati Milling Machine Company 

Chattering 

Probably the greatest annoyance to which users of Milling 
Machines are subjected, is the peculiar action called "chattering." 
This is a condition of vibration that sometimes is so serious as to 
affect the entire machine, and frequently gives the impression that 
it is caused by the driving gearing. This is hardly ever the case. 
Chattering always starts at the cutter, and whatever vibration may 
result from it in other members is due entirely to this intermittent 
motion of the cutter as it passes through the work and this motion 
carried through the spindle and gears causes a corresponding and 
exaggerated vibration in those members. We can not emphasize 
too strongly that chattering always starts at the cutter, although 
the fault may not always lie in the cutter itself. 

The action of the cutter at work is fully described in the chapter 
on An Analysis of the Process of Milling. Now, if the cutter can 
spring away from the work, or if the cutter is not properly sharpened 
so that it alternately digs in and then slides over the work again, 
it throws intermittent torsional strains on the arbor and these are 
carried through to the gears. 

When investigating the trouble it is well to make sure first that 
the machine is in proper adjustment, especially the spindle; that 
the arbor is properly fitted into the spindle and securely held there ; 
that the cutters and arbor supports are all as close to the end of 
the spindle as possible so as to keep the arbor from bending and 
springing away from the work; that the braces are properly attached 
and that the table, saddle and knee gibs are properly adjusted. If 
all these things are as they should be, the cause of the chatter lies 
either in the cutter, the method of mounting the cutter, the work 
itself, the method of holding the work, or a combination of some or 
all of these. 

Mounting the Work. The work should be mounted so as to 
bring the cutter as near the end of the spindle as possible and then 
the outer arbor support should be brought as close to the cutter as 
the work will allow. You can not get good results from a cutter 
held in the middle of a V arbor, 16" or 18" long, supported at its 
outer end only. The arbor should be as large as possible. The work 
must be securely held either in the vise or in a properly designed 
fixture, and the fixture itself must be strong enough to hold the 
work. 



A Treatise on Milling and Milling Machines 119 

We have known of serious cases of chattering that were caused by 
the operator having failed to carefully clean the fixture before 
inserting a new piece with the result that the piece rocked in the 
fixture. In another case, pieces made on an automatic machine 
were held in an excellent fixture made to fit the pieces and hold 
them securely, but serious chattering resulted from the fact that 
when adjusting the automatic machine which made the pieces, 
after the tools had been sharpened, the pieces were not made to the 
exact size as before, and therefore did not fit the jig. Although 
they were held down tight enough for the milling operation, they 
were not properly supported and this caused all the trouble. Yet our 
customer did not suspect this because he felt sure that the pieces were 
being turned to uniform size and shape. Sometimes the work itself 
is so frail that it springs under the cut and this induces chattering. 

When the arbor is of proper size and the cutters are properly 
mounted; the work of sufficient strength to stand the cut and 
securely held in proper fixtures, serious chattering may still result 
because of a faulty cutter. It is certain that if each tooth of a cutter 
has an opportunity to take an even chip of the same size, there will 
be no chattering provided that each tooth has an opportunity to 
take a chip of adequate thickness. Cutters with teeth close together 
are almost sure to chatter because the chip per tooth becomes so 
small that it is practically impossible for each tooth to take a chip. 
This condition is exaggerated if a slow feed rate is used. For instance, 
if we have an old-fashioned cutter with 16 teeth, feeding .008" per 
revolution, each one of these 16 teeth has a chance to take a maxi- 
mum chip only .0005" thick. It is not practical to grind a cutter 
that will run as accurately as this after it has been mounted on the 
arbor. Some of the teeth will therefore slide over the work. Even 
with all the other conditions as they should be, such a cutter is likely 
to cause those minute vibrations which produce the high pitched 
singing effect. 

If the feed in this case is increased to .030 or .040" per revolu- 
tion, the difficulty is quite sure to disappear. Again, an entirely 
new cutter of correct design may cause chattering because the 
cuttermaker, not knowing on what class of work the cutters will be 
used, usually grinds them with about 7° clearance. This is about 
50% more than it should be for cast iron and about twice what it 
should be for steel. Such a cutter having too much clearance will 
dig into the work and then spring back again at close intervals, 
causing the worst kind of chattering conditions. 



120 The Cincinnati Milling Machine Company 

Every new cutter should therefore first be properly sharpened 
for the work to be done. It sometimes happens that a cutter chat- 
ters when first put into the machine and after some use the chattering 
disappears. This is because the extreme cutting edge has been 
worn off a sufficient amount to reduce the clearance at the edge. 

One of the classes of milling that causes annoyance is milling 
key ways in shafts. These key ways usually are at the end of the 
shaft. The clamps are therefore some distance back from the end. 
The result is that when the cutter enters the work it lifts the shaft 
off the Milling Machine table, and of course, chattering results. 
On such work the trouble is exaggerated because usually milling 
cutters with side teeth are used. We recommend against this. 
A cutting-off tool in a lathe does not have side teeth, yet the action 
is the same. A plain milling cutter of proper width, with its sides 
very slightly hollow-ground will produce better results and the 
action of such a cutter will be still further improved if about two- 
fifths of the width of the teeth is ground off alternately so that 
each tooth will take a chip a little more than one-half of the width 
of the keyway to be cut. (See Chapter on Milling Cutters.) 

Frequently some degree of chattering is induced by the cutter not 
running true and it is not unusual for the user to feel that this is 
caused by either the hole in the spindle of the miller or the arbor 
not being true. This may be the case if the arbor and the hole in 
the spindle are not always carefully cleaned before inserting the 
arbor but the trouble is frequently due to the cutter teeth not 
having been ground true with the hole. 

Remedies for Chattering — Make sure that the machine is in 
proper adjustment all over; make sure that the arbor is of proper 
size; that its shank fits the hole in the spindle; that it is clean, and 
that the cutters are properly mounted and the arbor properly 
supported. The piece of work must be securely held and properly 
supported so it can not spring. If the cutter is the old-fashioned 
kind with teeth close together, grind out every other tooth. If the 
clearance angle is too great, reduce it. Cutters should be of the 
design as described in the chapter on Milling Cutters. These cut- 
ters used with a suitable feed rate are sure to eliminate chattering 
if other conditions are anywhere near right. If everything else 
appears to be in proper order, it is advisable to change the feed 
rate. Increasing the feed frequently improves the relation of each 
tooth to the size of chip that it takes to such an extent, as to stop 



A Treatise on Milling and Milling Machines 121 

the chattering action. All of the above refers to Milling Machines 
using cutters on an arbor. 

When face mills are used, particularly on Vertical Machines, 
too wide a cutting face on the teeth of the mills may cause chatter. 
The actual work of a face mill is not done by the face edges of the 
teeth, but by the peripheral edges. The face edges should therefore, 
not be too wide, or they will have a dragging action on the work which 
will induce vibration. These face edges should be only about ^" 
wide and the balance of the width of the blade should be ground 
back towards the center of the mill at an angle of about 7° (Fig. 114. 

Since chattering is really a synchronizing of the vibrations due 
to the different strains set up by cutting, it will sometimes be found 
effective to release some member, as for instance, one side of the 
brace, in order to break up this synchronism. Another point to 
be watched is the base of the fixture. It is not enough for the 
milling fixture to be strong enough to withstand the feed strain. 
It ought to be heavy enough to absorb the vibrations as dis- 
cussed in the chapter on Milling Fixtures, but it is proper to say 
here that the provision of adequate end supports and clamps will 
often do away with a good deal of chatter. This is particularly 
true of pieces which stand high above the table, in which case 
the pressures or forces resulting from the cut have a great moment 
around the knee. 




Fig. 114 

Outline of a properly sharpened face mill. 



122 



The Cincinnati Milling Machine Company 



CHAPTER V 
AN ANALYSIS OF THE PROCESS OF MILLING 

The preceding pages describe the various types of Milling 
Machines available for the work to be done in most machine shops 
and toolrooms. Bearing these machines in mind, we will proceed 
with an analysis of the process of milling and a discussion of the 
tools used. 

Milling is the removal of metal by means of a tool which rotates 
while the work is advancing or feeding in a direction at some angle 
with the axis of the tool. When we mill with an ordinary spiral 
mill, the axis of the tool is the center line of the arbor or spindle and 
the feed takes place at right angles to this axis. When we use a 
face mill on a Vertical Machine the axis of the tool is vertical, but 
the table again feeds at right angles to the axis. When we cut spiral 
gears the axis of the tool is the same as the axis of the spindle, and 
the table travels at an angle with this axis, but this time it is not a 
right angle. 



Classification of Milling Cutters 

The tools used for milling are called milling cutters. Milling 
cutters as we know them have a number of teeth, but it is not abso- 
lutely necessary that they 
should have a large num- 
ber; in fact, some milling 
cutters have only one tooth. 
Such cutters are called fly 
cutters. 

With the exception of 

fly cutters, all cutters are 

bodies of revolution. A 

body of revolution is a body 

F «g- 115 with such a shape that it can 

be formed in a lathe; in other words, a body which has a central 

axis. The simplest bodies of revolution we know are cylinders, 





A Treatise on Milling and Milling Machines 123 




Fig. 116 



cones and spheres, but a body of revolution may have any imaginable 
section. 

When such a body of revolution is provided with cutting teeth, 
it becomes a Milling Cutter. When the teeth are on the outside of 
the cylinder, as in Fig. 115, it 
is called a Spiral Mill. When 
the teeth are on the base of 
the cylinder, as in Fig. 116, it 
is called a Face Mill. 

When a face mill is of 
small diameter and of rela- 
tively great length, it is 
called an End Mill, Fig. 117. 
When the teeth are cut on a 
truncated cone, Fig. 118, it is 
called an Angular Mill; and 
when it is neither a cylinder 
nor a cone, but has an irreg- 
ular outline, it is called a 
Form Cutter, Fig. 119. 

From these five fundamental forms of cutters a great variety of 
shapes and styles of cutters for different purposes has been developed 

The Action of a Milling Cutter 

Most of the difficulties in milling arise from the peculiar shape, 
of the chip. The action of a milling cutter at work is therefore a 
very important thing to keep in mind. It will readily be seen with- 
out much discussion that the chip as taken by an ordinary milling 
cutter, a formed cutter or an angular cutter, is approximately of 

the shape as shown in Fig. 120, 

in the shaded portion. The 

cutter enters at A and leaves 

at B. When it enters, the chip 

has no thickness, theoretically 

speaking; when it leaves, the 

chip has its maximum thickness. 

Fig. 121 gives us a somewhat 

better idea of the shape of such a 

chip, but, whereas Fig. 119 completely overlooked certain things, 

Fig. 90 grossly exaggerates these same points. Here a milling cutter 




Fig. 117 



124 



The Cincinnati Milling Machine Company 





1050-A 




Fig. 118 



is shown with its center at Oi. This same cutter is also shown 
with its center at 2 , and it is supposed that the cutter has 
advanced in relation to the work from Oi to 2 during the time 
it made one revolution; in other words, that this distance Oi0 2 

is the feed per revolu- 
tion. (As a matter of 
fact, it is not the cutter 
which advances, but the 
work. However, the ef- 
fect is the same and the 
problem is simplified by 
assuming that the cut- 
ter has advanced as 
shown.) The cutter 
which we have repre- 
sented here is supposed 
to have only one tooth and this tooth is shown in the position it 
would be in when the center of the cutter has arrived at 2 . 
The line XY shows the top of the work when rough. The line 
VW shows the top of that part of the work which is finished. 
The curve YV has been swept out by the tooth of the milling 
cutter when its center was at 0^ It will be seen that the tooth 
ABC strikes the work at the point B, and that this point B is a 
little higher than the finished line VW. It will also be seen that 
at this moment the cutting edge of the tooth advances not only 
to the left, but also slightly downward, following the curve BR, 
and that it has to compress the metal of the work before it gets 
to the vertical position. 
This is not true cutting of 
metal because some of the 
parts of the metal have to 
be squeezed downward into 
the work. It is more like a 
punching operation. The 
metal has to flow away from 
the cutter to give the cutter 
a chance to enter. 

Fig. 122 gives a better and less exaggerated idea of what actually 
happens. The distance Oi0 2 is more than is ordinarily used 
in practice. It is true that such an amount of feed, or even more, 
is used per revolution, but not per tooth, and we are assuming a cut- 






Fig. 119 



A Treatise on Milling and Milling Machines 125 



£ 



Fig. 120 



ter that has only one tooth. Fig. 122 shows that the tooth enters 

almost, but not quite, in a vertical position, and that the height of 

this little hill as shown at B in Fig. 121, is very small indeed, and 

that, therefore, there is perhaps more of a chance that the cutter 

will slide over the metal to be removed than that it will penetrate. 

This is actually what happens in practice — the tooth does not 

penetrate at once, but slides over 

the work. In doing so, the cutter 

and the arbor are lifted or sprung 

up and put an increasing amount 

of pressure on the work. This 

pressure finally becomes great 

enough to make the tooth of the cutter penetrate into the metal. 

From that moment on the chip is being removed. 

There is something that makes the action described even more 
pronounced, and that is that a cutter is never absolutely sharp. 
However nicely a cutter tooth may be ground, it will be found that 
its edge is slightly rounded when viewed under a strong enough 
magnifying glass. 

It is obvious that such a rounding helps the tooth to slide over 
the work and delays the moment when the tooth actually begins 
to penetrate. 

All these things are not visible to the casual observer because 
the distances are so small and the cutter goes around so fast, but an 

analysis of the cutter ac- 
tion shows that these oc- 
currences must actually 
take place. 

Fig. 123 shows the cut- 
ter in various positions, 
each position being ahead 
of the previous one the 
amount of the feed per 
revolution. This sketch 
again is much exagger- 
ated to show that the 
finished surface as obtained is not an absolutely smooth surface, but 
has ridges running across. We are all familiar with these ridges. 
They determine the quality of the finish of the milled piece. It is 
plain that these ridges must be close together in order to give a toler- 
able finish. For mere roughing operations, the distance between the 




Fig. 121 



126 



The Cincinnati Milling Machine Company 




Fig. 122 



ridges is of no importance, but for finished work these ridges must 
be close together, and the better the degree of finish required the 
nearer these ridges must be to each other. 

Revolution Marks. These ridges are sometimes called "tooth- 
marks/ ' They are not toothmarks at all — they are revolution 
marks. If these marks were really toothmarks, then it would be 

possible to get the ridges very close 
together by simply putting more 
teeth in the cutter. However, as 
a matter of fact, the number of 
the teeth in the cutter does not 
affect the distance between these 
marks at all. This can be proven 
by putting two cutters next to each 
other on the same arbor. The cut- 
ters should preferably be of the 
same diameter and should have different numbers of teeth. They 
should be so placed that a pair of teeth are in line with each other. 
Then take a cut with both cutters at the same time over one piece 
of metal and you will find two important things. 

In the first place, the two cuts side by side have exactly the same 
number of ridges per inch, showing that the number of teeth has no 
influence. In the second place, you will find that the ridges made by 
the two cutters are not in line with each other, notwithstanding 
the fact that we took care to line up one tooth of the one cutter 
with a tooth of the other. 

Referring again to Fig. 123. The cutter positions are shown with 
a distance between them equal to the feed per revolution. We can 
calculate the height of the 
ridges if we know the 
diameter of the cutter, and 
the amount of the feed per 
revolution, and if we as- 
sume THAT THERE IS ONLY 
ONE TOOTH IN THE CUT- 
TER. The calculations show that for a 33^ ;/ cutter, and with a feed 
of fifty thousandths per revolution, the height of the ridge is .00019, 
or practically two-tenths of a thousandth; with a feed of thirty 
thousandths, it would be .00007, or less than one-tenth of a thous- 
andth; with a feed of twenty thousandths, it would be .00003, or 




Fig. 123 



A Treatise on Milling and Milling Machines 127 

three hundredths of a thousandth. Since there is only one tooth 
at work, it might be inferred that, if there were ten teeth, making 
the feed per tooth in the first instance not fifty thousandths, but 
only five thousandths, the height of the ridge would be much less 
than .00019". But this is not so, because a milling cutter never 
runs absolutely true. In order that a cutter shall run true every 
tooth of the 10-tooth cutter must be on exactly the same diameter, 




Fig. 124 

and describe a circle around exactly the same center, and in order 
to make this all perfect the cutter must be absolutely round; its 
hole must be absolutely round, its hole must be absolutely concen- 
tric with the outside; it must be mounted on an arbor without 
any clearance whatever; the arbor must be absolutely round and of 
even diameter; the center of the arbor must be absolutely in line 
with the center of its taper the taper must be absolutely round and 
must fit into the hole of the spindle which again must be absolutely 
round; this hole in the spindle must be absolutely concentric with 
the bearing of the spindle; this bearing must be absolutely round 
and must work without any clearance in the front box. This is a 
condition which is impossible. In a practical machine all of the 
points mentioned here will have some variation. The highest de- 
gree of workmanship would not avoid some little error in all of 
these places, and it is fairly certain that the resultant error will be 
an accumulation of some of these. 

If the sum of these errors is only two ten thousandths of an 
inch (and this would certainly be remarkably good workmanship), 
then the ridge made by the cutter will be two ten thousandths, 
regardless of how many teeth are at work. It is the swing of the 
cutter which makes the ridge. It is only then, when the swing of 
the cutter is less than two ten thousandths of an inch, that the 
ridge will be less deep. It is clear, therefore, that the ridge we see 
is a revolution mark and not a toothmark. 

However, if we should increase the feed per revolution to .300", 
then the height of the revolution mark would be approximately 
.0006", and in that case, it is very likely that the number of teeth 
in the cutter will reduce the size of the revolution mark. Fig. 124 



128 The Cincinnati Milling Machine Company 

represents revolution marks produced by an extremely coarse feed 
and is the picture of the inaccuracies of the cutter, arbor, spindle. 
etc., which produce the revolution marks, and superimposed on 
this are slight depressions representing the toothmarks. It must 
be remembered that this represents a cut taken with an extremely 
fast feed per revolution, and that the faster the feed per revolution. 
the more pronounced the toothmarks will become. 

An analysis of the action of the cutter will show that the tooth 
immediately following the low one (corresponding to the high point 
on the curve) will reduce the height of the revolution mark some- 
what, making it less than the amount actually represented by the 
error in the cutter, arbor, spindle, etc., but it must be noted that 
even in these extreme cases the principal mark left on the work is 
the revolution mark, although the cutter no longer acts as if there 
were only one tooth. 

With a fine feed per revolution, such as is more generally used. 
the cutter does act, so far as marking the work is concerned, as if 
it had only one tooth. 

Referring again to Fig. 121, it will be seen how difficult it must be 
for the tooth of the cutter ABC to penetrate into the metal. 
The conditions shown here are worse than found in actual practice, 
but only in amount; the nature of the conditions is the same. If 
we should make the tooth in the form A^BC, then it would be 
easier for the tooth to penetrate; there would be no necessity for 
the tooth to compress the metal downward, and there would be a 
true cutting action, such as we get with a lathe tool. This form of 
tooth would have a face which is not radial, but points back of the 
center; in other words, the tooth is undercut; or to express it as 
we do with lathe tools, the tooth has rake. Using a cutter with 
rake makes the action much easier. We will treat this subject 
more at length in the chapter on Milling Cutters. 

Action of a Face Mill. In the previous paragraphs we have 
studied the action of the teeth of ordinary milling cutters, but this 
is not the action of the teeth of face mills or end mills. The tooth 
of a face mill acts like a planer tool, or shaper tool, the only difference 
being that instead of moving over the work in a straight line, it 
moves in a circle. 

Fig. 125 shows a section of a face mill, the body shown in cross- 
section lines and two teeth projecting. XY is the top of the 
rough work, and VW is the top of the finished part of the work. 



A Treatise on Milling and Milling Machines 129 




D'RECTiON OF FEED 



Fig. 125 



The work feeds against the cutter in the direction of the arrow. It 
will be seen at once that it is the peripheral edge of the tooth that 
does the work, taking away a slice every time a new tooth enters, 

as shown in cross-section, 
two slices having been 
represented in the sketch. 
It is often thought that 
the face edge of the 
tooth of a face mill does 
the cutting, but this is 
not so; the sketch shows clearly that the cutting is done by the 
peripheral edge of the tooth. 

Fig. 126 is a top view of this same face mill with one tooth 
shown in position. BW is the portion of the work already trav- 
ersed by the tooth and XY is the metal about to be cut off. The 
cutter turns in the direction of the arrow, and takes a slice as 
shown in cross-section. In order to have a true cutting action, 
the line AB of the cutter tooth must clear the already finished 
portion, and the line BC must 
fall back of the center, the angle /° 
OBC being called the rake, and \ 
the angle ABD the clearance 
angle. These rake and clearance 
angles may vary for different 
kinds of material and different 
conditions, but there must be 
some clearance angle or else the 
cutter will refuse to cut, and if 
we wish to cut with some degree 
of efficiency, there also must be 
a rake angle, else the metal will 
be pushed off (the action of a 
punch) instead of being cut off (the action of a knife). 

The chips made by a properly designed face mill resemble planer 
chips; in fact, it would be impossible to say what machine has 
produced the chip by simply looking at it; but, if the cutter is not 
properly designed, then the chips produced will be short and badly 
crushed — entirely different from those produced by a proper planer 
tool. 

The power required to remove metal will be very much more 
if the proper angles are not provided, and the life of the cutter. 




Fig. 126 



130 



The Cincinnati Milling Machine Company 



and, for that matter, the life of the machine also, will be very much 
shortened. 

Action of a Side Mill. A side milling cutter has both peripheral 
and side teeth. It is a fact, however, that the greater part of the 
cutting is done with the peripheral teeth, unless the amount of stock 
to be removed is very small. Fig. 127 shows a Side Milling Cutter at 
work on a piece of material cutting on both periphery and side. 

The amount of metal to 
be removed is indicated 
by the dotted lines. Sup- 
pose the thickness of this 
stock is Y" and the other 
dimensions as given in 
the figure; at a speed of 
70 feet per minute, we 
run 54 revolutions per 
minute. If the feed is 
very fast, say, 20" per 
minute, there will be re- 
moved per revolution 
tI, and as there are 11 
teeth, each tooth has a 
feed of 5%, or practi- 
cally l /so r . It will be seen that at the bottom of the groove, and 
for a width of %", the cutter acts exactly as a spiral mill; that 
is, it does all the cutting with its peripheral teeth and removes a 
comma-shaped chip which is 1 / 30 " thick at its thickest part. For 
the other Yi' of the width of the cut, the cutter also acts like a 
spiral mill, the only difference being that here the cut is Y" deep 
instead of Y"- The surface traversed by each side tooth is Y" 
high and 1 / 3 o" wide, that is, it is as wide as the chip is thick. This 
area therefore is * / 60 of a square inch. The surface traversed by the 
peripheral edges of each tooth consists of two parts; one part is 
Y" wide and Y" high; the other is Y" wide and Yi high- The 
first part has an area of Y x Y equaling ^ square inches, and the 
other part has an area Y x Ys equaling -^ square inch, altogether 
-^ square inch, therefore it traverses practically nine times as much 
surface as a side tooth. If the feed were less than 20" per minute, 
the surface traversed by the side teeth would be proportionately 
smaller. It will be seen then that the side teeth perform only a 
small portion of the total work, and their only function is to clean 




Fig. 127 






A Treatise on Milling and Milling Machines 131 

up the side of the groove or slot, thus acting merely in a finishing 
capacity, and at the same time, of course, provide space for the 
accommodation of the chips produced. 




Fig. 128 

AN ILLUSTRATION OF LARGE SIDE MILLS IN ACTION 



The mills in Fig. 128 are 133/£" in diameter, and, in combina- 
tion with a pair of spiral mills 3" in diameter, they take a cut f/g" 
deep across these surfaces, having a width of 273^ /r at a table travel 
of 4^4" Per minute. They work at a speed of 14 r. p. m. and re- 
move altogether 11 3^" of metal per minute. A final finishing cut 
brings the pieces accurate to within .001". 

The work is done on a No. 4 Plain High Power design miller. 





~li 














~,i. 


r.*i 


r±- 


«i- 






A 

7 





4-74— U 



Fig. 129 



132 The Cincinnati Milling Machine Company 



CHAPTER VI 

MILLING MACHINE FEEDS 

The feed of the Milling Machine is the movement of the table 
which advances the work against the cutter. On knee and column 
type machines there are three possible movements of the table; 
namely, lengthwise of the table (longitudinal feed), crosswise of 
the table and vertical. In some machines all three feeds are auto- 
matic; that is, they are power-driven, but in quite a large number 
only one power feed is provided, namely, the longitudinal feed. 

Two Systems in Use. There are two well-known feed systems 
in general use — feed in thousandths of an inch per revolution of 
spindle, and feed in inches per minute. With the first system the 
feed is driven from the spindle, so that when the spindle speed is 
increased, the amount of feed per minute will be increased in pro- 
portion, but the ratio between the advance of the table and the 
feed of the cutter will remain the same. The distance between 
revolution marks will therefore remain the same. With the second 
system, the feed is arranged in such a way that for any given position 
of the feed lever there is a fixed amount of feed per minute, regard- 
less of how fast the spindle runs. A change in spindle speed will 
not affect the quantity of output unless the feed rate is also changed 
at the same time. 

Standard American practice is to make all Cone-Driven Millers 
with the feed driven from the spindle, and therefore, reading in 
thousandths of an inch per revolution of the spindle. It would be 
difficult to arrange such machines with feeds reading in inches per 
minute, because to do this requires a constant speed shaft to drive 
from and there is no constant speed shaft on a Cone-Driven Miller. 
Cincinnati Cone-Driven Millers are provided with 16 feed changes, 
ranging in the smaller machines from .006 to .250 of an inch per 
revolution, and in the larger sizes from .007 to .300 of an inch per 
revolution of spindle. 

Standard practice on Millers with constant speed drive is to 
arrange the feed to read in inches per minute. This is a simple 



A Treatise on Milling and Milling Machines 133 

matter on these machines, because the main shaft always runs at 
constant speed and the feed is driven from it. There are some 
advantages in the older system used on Cone-Driven Machines, 
but except in special cases, these advantages are outweighed by 
those of the newer system, reading in inches per minute, as will be 
seen from what follows. 

Feeds in Thousandths per Revolution. Let us first con- 
sider a machine with feeds reading in thousandths per revolution. 
Assuming a small end mill requiring a fast speed, say 350 r. p. m. 
The finest feed available on a large Cone-Driven Machine is .007 
per revolution. On some work this feed may be entirely too fast 
for this small, frail cutter. 

Now, let us assume a large cutter requiring a slow speed, say 
14 r. p. m. The coarsest feed is .300 per revolution, and the fastest 
table travel we can get at 14 r. p. m. is 14 times .300" or 4.2" per 
minute, which is entirely too slow in many cases. These extreme 
cases indicate the limitations of this system. Most milling comes 
between these extremes and for the usual work the feeds provided 
are entirely satisfactory. This system has the advantage that it 
indicates at once the grade of finish; that is, the distance between 
revolution marks. 

Feeds in Inches per Minute. Let us consider a machine with 
feeds in inches per minute. Assume again a small end mill running 
350 r. p. m. The finest feed on Cincinnati High-Power Millers is 
Yi' per minute. This results in the present case, in a feed of about 
.0015" per revolution, certainly fine enough for the frailest cutter. 

Now assuming a large cutter at 14 r. p. m., using the coarsest 
feed of 20" per minute. We, of course, get a table travel of 20" per 
minute, which is a very satisfactory rate of production. This system 
also has the advantage of indicating at once the rate of production. 
Cincinnati High-Power Millers are all arranged with feeds reading 
in inches per minute, the feed box providing 16 changes, ranging 
from l /2 f to 20" per minute. 

Influence of Feed on Production. The rate of production 
depends directly on the rate at which the work passes under the 
cutter. It follows, therefore, that the feed used should be as fast as 
practical. There are certain conditions which frequently arise in 
practice, which limit the rate of feed that can be used. Quite often 
the piece is of such a nature that it can not be held rigidly in the 
holding fixture. In still other cases the piece itself may be too frail 



134 The Cincinnati Milling Machine Company 

to stand the pressure due to a heavy feed. In such cases there are 
only two things possible j either reduce the feed (table travel) and 
do the work slower, or if the machine is cone-driven, reduce the 
feed per revolution and increase the speed. On a High-Power 
Machine this latter result is accomplished by simply increasing the 
speed of the cutter, because this automatically reduces the feed per 
revolution, therefore, producing smaller chips and consequently 
less pressure against the work. However, high speeds have a 
tendency to burn out the cutter, and therefore, if we want to increase 
production by increasing speeds, we must do something to keep the 
cutter from burning. This will be discussed more fully in the 
chapter on Stream Lubrication. 

Roughing and Finishing Cuts. Some work is milled with only 
one cut to produce the desired surface. Other work requires two 
cuts. In the latter case the roughing cut may be taken without 
regard to the finish produced, and the only elements to be con- 
sidered are : the strength of the piece itself, the power of the machine, 
its ability to stand the strains and the condition of cutter, arbor 
and fixture. If only one cut is taken, then the finish must also be 
considered. Using spiral mills, end mills or formed mills, a very 
satisfactory commercial finish is produced with from .035 to .050" 
per revolution. Such a feed, and often even higher feeds may be 
used for surfaces which are bolted together and which are not re- 
quired to be oiltight, but for a great variety of work, a finer feed is 
necessary. Work which must be scraped or which is finish ground 
will easily stand .030", whereas work which must have a high finish 
and does not get any subsequent operation may require a feed as 
low as .020" per revolution. When very small end mills are used for 
such work as die sinking, and rounding out the ends of key ways, 
and various other delicate operations, a finer feed must be used, 
not because of the finish, but because of the frailty of the cutter. 

The relation of feed to speed on a great variety of cuts in cast 
iron and steel is given in the diagrams in the following chapter on 
Speeds of Milling Cutters. 



A Treatise on Milling and Milling Machines 135 



CHAPTER VII 

SPEEDS OF MILLING CUTTERS 

We are all familiar with the fact that if a piece of work in a lathe 
runs too fast, the lathe tool will burn out. This term ' 'burning out" 
is incorrect. What is meant is, that the tool becomes so hot that the 
temper of the extreme cutting edge is drawn out, and this edge be- 
comes so soft that it refuses to cut further. This holds true whether 
the tool is a lathe tool, a planer tool, or a milling cutter, the only- 
difference being that with the lathe and planer tool the work moves 
while the tool is fed into it, whereas with the milling cutter the 
condition is reversed — the work is fed under the cutter while the 
milling cutter rotates. A milling cutter is a complicated tool as 
compared with a lathe or planer tool and we will therefore use the 
latter in our analysis of the action of cutting tools. 

Action of a Lathe Tool. When a lathe tool takes a chip, 
feeding, say, from right to left, its front end is up against the finished 
part of the work, its top face is partly covered by the chip as it 
comes off the work, and its left side is pressed against the work 
trying to feed into it. There is considerable pressure between the 
work and the front edge, heavy pressure between the top and the 
chip, and also heavy pressure between the left side and the work. 
Meanwhile the work is moving and this movement under pressure 
causes friction and friction generates heat. It can be easily seen 
under a magnifying glass that the chip as it comes off the work is 
broken up into a great number of fine laminations which slide over 
each other. The breaking up of the chip and the sliding of the 
laminations both generate heat. 

Heating. If a lathe tool takes a chip y% deep with a feed of ^2" 
per revolution, the chip as it comes off has a section much greater 
than y% x yz" , and a different shape; it is not rectangular, but 
triangular. All this breaking up, sliding, and changing of shape 
causes a great deal of heat to be developed. In fact, much less than 
1% of all the work done on a lathe is used for separating the chip 
from the work, and all the rest of the work is spent in breaking up 



136 The Cincinnati Milling Machine Company 

the chip, overcoming the friction between tool and work and between 
tool and chip. At the same time this useless work is converted into 
heat, which heats up the tool. Of course, the tool loses some of this 
heat. If we run at a low speed, taking a fine chip, and using a fairly 
large tool,, the amount of heat generated is relatively so small that 
the tool can carry it off and conduct it into the body of the machine or 
radiate it out into the atmosphere as quickly as it receives the heat. 
It warms up a certain amount until its rate of radiation and con- 
duction are as great as the rate at which it receives heat. 

From that moment on the tool does not become any hotter, 
regardless of how long we keep on cutting. If we should cut faster 
or take a heavier cut, then the tool will become much wanner before 
this equilibrium is reached. If we go still further increasing the speed . 
we finally reach the point where the tool receives more heat than it 
can dissipate., and then the tool '''burns out." We find, however, 
that the body of the lathe tool is perhaps slightly warm, but cer- 
tainly not hot. showing that this body had ample capacity to carry 
off all the heat generated. Why then does the tool burn out? 

Imagine that we cut a lathe tool up in slices,, starting at the shank 
end and proceeding toward the cutting edge. The sections become 
smaller and smaller, and the section close to the cutting edge is very 
small. This last section, therefore, can not carry off much heat, 
and besides being completely covered by the work and chip can not 
radiate heat. In fact, it is protected because both chip and work 
themselves are hot and may even add to the heat of the tool. We 
find, moreover, that it is only the extreme cutting edge which is 
affected. 

Application to a Milling Cutter. All that was said about a 
lathe tool is applicable to a milling cutter. A milling cutter has an 
advantage in so far that the tooth of the milling cutter stays in the 
work for only a short time and then rotates through the air, giving 
it a chance to cool down. If the cut is shallow, the tool is in the 
work for only a short period of time. If the cut is deep the con- 
ditions are somewhat less favorable, but in almost all cuts the period 
of time during which it cools in the air is much greater than the 
period of time during which it accumulates heat. If a milling cutter 
is properly designed and made it is possible to run it at a higher 
rate than a lathe tool. Unfortunately, most milling cutters are 
made without rake, and must do three or four times as much work 
as a lathe tool in order to remove the same amount of metal. All of 



A Treatise on Milling and Milling Machines 137 

this extra work is converted into heat, and this more than offsets 
the favorable conditions under which a milling cutter works. 

The speed of a tool is limited by the fact that it gets so hot that 
it loses its temper, and this heat is developed by useless work being 
done, namely, by bending and breaking up chips, and so on. There 
are three different ways by which we could speed up a tool. 
One, by finding some material of which to make the tool which 
would not lose its temper no matter how high the temperature. 
This was partly accomplished by the invention of high-speed 
steel. A second way, by making a tool of such shape that it merely 
separates the metal and performs no useless labor. Such tools may 
be invented some day, and, in fact, a lathe tool has been made which 
will remove metal without breaking it up. A third way to increase 
the speed would be to carry off the heat as fast as it is generated. 
If we can do this, then it makes no difference how much heat is 
developed by the action of cutting, for all of this heat will be carried 
off immediately and the tool will become no hotter. Under such 
conditions, as far as burning out is concerned, ANY speed would be 
permissible. 

To obtain the very best results we should employ all three of 
these methods; that is, we should have the cutter made of some 
material which will retain its temper even at a high temperature; 
it should be constructed in such a way that it does as little unneces- 
sary work as possible, and there should be means of carrying off 
the heat as fast as it is generated. Under these conditions we can 
get the highest possible speeds. 

Conditions Determining Proper Speeds. It is impossible 

TO STATE DEFINITELY AT WHAT SPEEDS CUTTERS SHOULD BE RUN, 
BECAUSE THIS DEPENDS ON TOO MANY CONDITIONS. It depends in 

the first place on the kind of cutter, in the second on the amount of 
material to be removed per minute and, not only that, but it depends 
on the relation between the depth of cut and feed. A cut of y% " 
depth and y% feed per revolution can be taken at a higher speed 
than a cut at a depth of x /±' and with a feed of yz" per revolution, 
though the amount of material removed per minute would be the 
same in both cases. It further depends very largely on the rigidity 
of the machine and the fixture in which the piece is held. It depends 
also on the rigidity of the piece itself, and last, but not least, on 
how often we think it economical to regrind the cutter. 

We can run at almost any speed if we are willing to regrind 



138 The Cincinnati Milling Machine Company 

the cutter every five minutes, but this would not be economical. 
It is also possible to regrind the cutter only once every six months, 
but we would have to run so slow that again this would not be 
economical. There is a point where we get the highest efficiency 
and when a shop has to mill a great number of pieces of one kind, 
a few figures should be put on paper to determine which is the most 
economical speed at which to run the cutter. 

Influence of Speed on Production.* To illustrate: A shop 
has to mill 1,000 pieces, and employs two cutters for this purpose, one 
of which is being reground while the other is in action. We run at 
such a speed that it takes six minutes to mill one piece. We will 
assume that it requires three minutes to place the piece in the jig 
and remove it again, 60 minutes to regrind a cutter, and 40 minutes 
to reset the machine while the new cutter is put in place. Assume 
that the speed is such that the cutter must be reground after every 
100 pieces. We then have 3,000 minutes to put them in the fixture, 
6,000 minutes to mill them, 600 to grind the cutter and 400 to set the 
cutter. While the grinding of the cutter is being done, the milling 
still goes on, so that though we have to figure in the labor cost of 
grinding the cutter, the milling machine is never standing idle, 
except during the time that we reset the machine for the new cutter. 
The total time, including sharpening and setting cutters for these 
1,000 pieces is 10,000 minutes. (The machine time is 9,400 minutes 
and the grinding time 600 minutes.) 

If we should run the cutter so much faster that the milling could 
be done in five minutes instead of six minutes per piece, under those 
conditions we have to grind the cutter more frequently than once 
in every hundred pieces, as in previous examples. Let us assume 
that X represents the number of times we must grind the cutter per 
hundred pieces, then we would like to know how often we may 
grind this cutter without losing time. In order not to lose time we 
must mill all these 1,000 pieces in 10,000 minutes, and we must 
remember that if we grind the cutter X times as often, we also must 

*In order to keep this illustration as simple as possible, so that the principle 
involved may not be confused with the wage factor, it is assumed that the 
value of an hour's work on the cutter grinder equals that of an hour's work 
on the milling machine. If, in the illustration which assumes the use of only 
one cutter, the milling machine operator also does the cutter sharpening, the 
result appears to be better, because the operator is not idle, but the milling ma- 
chine is idle and milling production suffers. The important thing is to keep 
the milling machine going at the right rate, and as nearly continuously as 
possible. 



A Treatise on Milling and Milling Machines 139 

reset the machine X times as often. The cutting now takes place 
in 5,000 minutes. It takes 3,000 minutes to put the piece in the 
fixture; X times 600 minutes to grind the cutter; X times 400 
minutes to reset the machine; altogether 10,000 minutes. 

5,000+3,000+400 X+600X = 10,000. Therefore, X = 2. In other 
words we may grind the cutter once for every 50 pieces. The machine 
time in this case is 8,800 minutes and the grinding time may be 
1,200 minutes. 



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Roughing cast iron. 



This means if we reduce the cutting time from six minutes to 
five minutes, we may grind the cutter twice as often as before and 
not lose time. If we find that we have to grind the cutter less than 
twice as often, we would gain time, but if we find that we have to 
grind the cutter more than twice as often, we lose time. 

The figures show a rather striking result. A reduction of the 
cutting time from six minutes to five minutes, that is, an increase 
in speed of 20%, would allow us to regrind the cutter twice as often 
provided we had two cutters. If we increase the cutting speed so 
as to reduce the cutting time from six minutes down to four minutes, 



140 



The Cincinnati Milling Machine Company 



we might grind the cutter three times as often and not lose time. 
If we had only one cutter the machine would stand idle during the 
additional time that the cutter is being reground and we would 
get an equation very similar to the previous one, except that we 
must figure in the time during which the machine stands idle, 
which is just as long as the time during which the cutter is being 
reground. Assuming that the machine and operator are both idle 



480 




60 80 

CUT SPEED 

Fig. 131. Spiral Mills 

Roughing re" deep, cast iron. 

while the cutters are being ground, then the machine time (which 
includes the times the machine is actually milling, is standing still 
for the cutter to be removed and reset, and standing still while the 
cutter is being resharpened) is 10,000 and grinding 600 as before, 
making the total time 10,600. This equation then would be: 

5,000+3,000+400 X+600 X = 10,600, and therefore, X = f§ or 
±$ 

8 • 

In other words, under those conditions, we may regrind the 
cutter only one and five-eighths times as often as before. 

It will be readily seen that if it takes a longer or shorter time to 
grind a cutter or to reset the machine, and if the proportions between 



A Treatise on Milling and Milling Machines 141 



chucking time and cutting time are different, the value of X will 
be different also. 

In our own practice parts are made in comparatively small 
lots — several hundred at a time — and we aim to use such a com- 
bination of feed and speed as will enable the cutter to stand up for 
one complete lot of pieces without resharpening. 



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60 80 

CUT SPEED 

Fig. 132. Spiral Mills 

Roughing Y% deep, cast iron. 

Practical Cutting Speeds. The diagrams, Figs. 130 to 142, 
were developed from our own practice. 

We make parts in comparatively small lots and plan our feeds 
and speeds so that a cutter will mill a complete lot without resharp- 
ening. The life of the cutter is therefore a factor entering into 
these curves. They are applicable to modern machines equipped 
with the latest design cutters and ample lubrication, where lubricant 
is used. They do not show the maximum feeds and speeds that can 
be used, but are a safe guide for those who are responsible for pro- 
duction. It is entirely practical to very greatly exceed these feeds 
and speeds on some work, but if the equipment consists of the usual 
form of standard cutter as found in stock, it is necessary to reduce 



142 



The Cincinnati Milling Machine Company 



the results shown by these speed curves a very substantial amount 
before they can be applied. 

Roughing Cast Iron with Spiral Mills. The diagram in Fig. 
130 shows cutting speeds and feeds when milling cast iron at different 
depths of cut with a 3" diameter cutter. The variables are the depth 
of cut. the feed in inches per minute., and the cutting speed. That 
part of the curves shown to the right of the heavy vertical line 



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100 



drawn at 70 feet per minute cutting speed, represents good practice. 
The use of these curves will be evident from the following: 

Suppose we are to take a cut J $" deep in cast iron and wish to 
run 80 feet per minute cutting speed. The curves will show that the 
most efficient feed rate to be used., providing the work and cutter 
will stand it. is 22" per minute. On the other hand, suppose we have 
a piece of work which we feel should go through the machine at a 
feed of 12" per minute. If the cut is again -^" deep, we may run as 
fast as 88 feet per minute cutting speed. It must be noted that the 
above diagram does not take into account that influence the diameter 



A Treatise on Milling and Milling Machines 143 

of the cutter has on the permissible speed. It is good for cutters 
from 3" to 3}// in diameter. 

The diagrams in Figs. 131, 132, 133 and 134 should therefore 
be referred to for more exact results for cutters of other diameters. 

The curves in Fig. 131 are based on cuts jt " deep. Now, assuming 
a cutter 4" in diameter and a roughing cut at .240'' per revolution: 
It will be safe to run the cutter 92 feet per minute. Similarly, the 

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curves in Fig. 132 show that under these same conditions and with a 
cut y% deep, the best cutting speed is 84 feet per minute. 

Fig. 133 shows that with a cut -V' deep the best speed is 76 feet 
per minute, and Fig. 101 shows that with a cut y deep the best 
speed is 65 feet per minute. 

These figures show a range in speed from 65 to 92 feet cutting 
speed. Generally speaking, 70 to 75 feet cutting speed is good 
practice when milling a high-grade of cast iron, such as is used in 
the better class of machine tools. 

The above curves are based on wide spaced, wide angle cutters. 



144 



The Cincinnati Milling Machine Company 



When using these curves in connection with the older form of 
standard cutters as found in stock, the results shown on these 
curves should be reduced to from one-third to one-half of their 
values before applying them. 

Finish Milling Cast Iron Using Spiral Mills. Fig. 135 
shows curves based on good practice for finishing cuts ^x" and ^2" 
deep, but this again does not take into consideration the influence 



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Fig. 135. Spiral Mill j 

Finishirur, cast iron. 



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of diameter of cutter. These curves are a good guide for general 
practice. For more exact results, refer to Figs. 136 and 137. which 
are based on the use of cutters of different diameters. The values 
of these curves shown between the heavy horizontal lines drawn 
at .050" and .060* per revolution indicate the feeds and also the 
corresponding speeds which we consider good practice for finishing 
cuts on surfaces which will afterwards be polished. For producing 
the finer grades of finish, suitable for scraping, the values of the 
carves shown between the horizontal lines drawn at .024" and .030* 
feed per revolution should be used. If the cutters are sharp and the 



A Treatise on Milling and Milling Machines 145 

equipment is in good order, this feed rate will produce an excellent 
finish. 

Assuming again our 4" diameter cutter and a feed of .023" per 
revolution : Fig. 136 shows that with a finishing cut £$" deep, it is 
safe to run the cutteTs 130 feet per minute, and Fig. 137 shows that 
for a finishing cut &' deep, it is safe to run the cutters 120 feet 
per minute. 



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Finishing ^" deep, cast iron. 



Speeds and Feeds for Shell End Mills. The diagram, Fig. 
138, shows curves based on good practice when using end mills, 
taking cuts from y% to ■/§" deep in cast iron. In all of these curves 
the depth of cut remains constant, the variables being as before, 
the feed in inches per minute, the cutting speed and diameter of 
the cutter, and there is also the additional variable, width of cut. 

We find from these curves that if we want to take a cut 2" wide 
with a3" diameter end mill, we can run about 75 feet cut speed and 
at a feed of 11 ;/ per minute. Should we wish to take a cut 3" wide, 
with a 33^" diameter cutter, we find that we can run practically 
60 feet cut speed and use a feed of 93^" per minute, and so on. 



146 



The Cincinnati Milling Machine Company 



A very interesting additional feature of these curves is found 
below the 50-foot cut speed curve, the application of which is as 
follows: 

Suppose we are taking a cut 2y 2 " wide with a 23^ " diameter 
cutter at 50 feet cut speed. We can feed safely 63/9" per minute. 
However, if for some reason we should find it preferable to feed only 
3" per minute, then we can run 100 feet cut speed with safety. In 
the same way, with a Zy 2 " diameter cutter, taking its full width 




60 



80 (00 

CUT SPEED 



20 



Fig. 137 

Finishing 



Spiral Mills 

deep, cast iron. 



of cut, namely % l A", the proper speed is 50 feet and the corresponding 
feed is Sy\ However, at 5J^ ;/ per minute feed on this same cut, 
we can with safety run 80 feet cut speed, and so on. From this it 
will be seen that all of the diagram lying above the 50-foot cut speed 
curve shows the relation between feed, speed, diameter of cutter 
and width of cut. That part of the diagram which is below the 50- 
foot curve applies only to the maximum width that each cutter 
can take, it of course being clear that a3" diameter end mill can not 
take a cut greater than 3" wide. This part of the diagram is useful 
in showing the extent to which the cut speed may be increased when 



A Treatise on Milling and Milling Machines 147 



the feed is reduced, the diameter of the cutter and the width of cut 
remaining constant. 

This diagram is based on actual practice in our shop, using 
modern wide-spaced shell end mills. For the older style of end 
mills as found in stock, the values shown by these curves should be 
reduced by 25% to 35%. 



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WIDTH OF CUT 
Fig. 138. She!! End Mills 

Broken corners. Roughing, cast iron H"-^" deep. 

Face Milling Cast Iron. Fig. 139 shows a set of curves for 
High Power Face Mills and Standard Face Mills for both roughing 
and finishing cuts which have a width approximately equal to the 
diameter of the cutter. From these we find that at a feed of 12" 
per minute a High Power Face Mill can very safely run 62 feet 
cutting speed for roughing and 82 feet for finishing. A Standard 
Face Mill, that is, one of the lighter design, should run about 50 
feet cutting speed for roughing and 73 feet for finishing, and so on. 
At a feed of 8" per minute, the speeds become for a High Power 
mill 68 feet for roughing and 89 feet for finishing, and for a 
Standard mill, 56 feet for roughing and 79 feet for finishing. 

Spiral Milling in Steel with Stream Lubrication. Fig. 
140 is a general diagram based on cuts ^y, y, ^" and 34" deep, 



148 



The Cincinnati Milling Machine Company 



taken with a wide spaced, wide angle spiral mill with rake, in cold- 
rolled machinery steel with an ample supply of cutting lubricant. 
Assuming a feed of 8" per minute, the corresponding speed for a 
cut 34" deep is 62 feet; for ^" deep, 80 feet; for J 
and for y&" deep, 128 feet per minute. Finishing cuts 
deep in machinery steel under the above conditions of ample lubri- 
cation, should under good shop conditions be taken at a cutting 



xs" deep, 104 feet, 



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CUT SPEED 

Fig. 139. Face Mills 

Roughing and Finishing, cast iron. 
Depth of cut, roughing y 6 to %, finishing -^ to tr. 

speed of 150 to 160 feet per minute. When the equipment consists 
of the older form of cutters, such as can be bought from stock, and 
the lubricant is used in limited quantities, the above figures should 
be reduced to from ^ to 3^ of the values shown in the curves before 
they are applied. 

Face Milling Steel. Fig. 141 is used in exactly the same way 
as Fig. 106, except that it shows the relation between feed and speed 
when milling steel, whereas Fig. 139 applies only to cast iron. This 
diagram is again based on roughing cuts from %" to &* deep, and 
finishing cuts ^ r/ to & deep on cuts having a width equal to from 
y 2 " to %" the diameter of the cutter. 



A Treatise on Milling and Milling Machines 149 



If we want to take a roughing cut at 16" per minute the diagram 
shows at once that we can use about 80 feet cut speed. A finishing 
cut at 16" per minute can be safely taken at 94 feet cut speed, and 
so on. 

The separate curve at the left of the diagram applies to rough- 
ing cuts 34" deep and 6" or more in width. These exceptionally 
heavy cuts of course can not be taken at such high speeds and fast 













































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80 
CUT SPEED 



100 



120 



140 



Fig. 140. Spiral Mills 

Machinery steel. Stream lubrication. 

feeds. For instance, at a feed of 12" per minute the cut speed 
should not be more than 60 feet. 

Keywaying. Fig. 142 is again based on modern cutters supplied 
with ample lubricant and milling nickel steel drop forgings 1 }/£% N., 
.30 to .40 carbon, .40 to .60 Chr., and also when milling the grade 
of machinery steel known as hub stock. There are two sets of 
curves shown. We will first consider the curves based on a 2%" 
diameter cutter. This is a cutter of our latest design, as described 
in the chapter on that subject, and it will be seen that with a 
feed of 8" per minute, a cutting speed of 30 feet can safely be used 
in chrome nickel steel, and in hub stock a cutting speed of 73 feet 



:■:■: 



'he Cincinnati Milling Machine Company 



-i : ::." :izhz. With cutters of the older design these results 
should again be reduced. 

The other two curves, which refer to a special staggered tooth 
cutter, are based on the use of the cutter shown in Fig. 143. This is 
:-. ;u~£7 4' in diameter. &" face, with inserted teeth, as shown. 
Its construction makes it possible to take advantage of the best 
cutting angles and it will be noted that the teeth are far apart and 



a- 




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sc 




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CUT SPEED 

Fig. 141. Face Mills 

3 keel castings and machinery ateel. 
Width of cut, J-2 ^o ^i the diameter of the cutter. 

: : :th removes a chip which is only part of the full width of 
the cut. It therefore has not only a free cutting action, but the chips 
are entirely free to get out of the way throughout all stages of the 



Referring to the diagram, it will be seen that at 8" per minute 
feed this cutter mills chrome nickel steel safely at 102 feet cutting 
speed, and a corresponding increase over the other cutter when 
milling hub stock. These curves and this cutter are shown to indi- 
cate what ~;i£ meant in a preceding paragraph which stated, 
that for special cases, the speeds and feeds given in these curves 
can be very greatly exceeded. 



A Treatise on Milling and Milling Machines 151 



The Cincinnati Milling Machine Company recently carried out 
extensive experiments to determine maximum cutting speeds that 
could be taken with a modern milling machine equipped with 
proper cutters and provided with ample cutting lubricant or coolant 
properly applied. Machinery steel was cut at speeds of 400 to 450 
feet per minute when taking cuts not deeper than }/%, 250 to 350 
feet per minute when taking cuts 34" deep, and keyways %" wide 
and 3 s " deep were milled at a cutting speed of 400 feet per minute. 



tM _ n _ _ _ - _.^_ _ ___ 


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40 60 

CUT SPEED 



80 



IOO 



\20 



Fig. 142. 

Machinery steel. 



Keywaying 

Stream lubrication. 



Nickel steel, heat-treated, was milled at 150 feet cutting speed, 
taking cuts %" wide, V/ deep. 

Vanadium steel of great hardness was milled at a cutting speed 
of 190 feet per minute. 

Tool steel, 1.25% carbon, such as is used for certain classes of 
reamers, was milled at a cutting speed of 200 feet per minute. The 
results of these tests are given in detail in Chapter VIII, on Stream 
Lubrication. 

Safe Practical Speeds. In general practice the following 
cutting speeds can be safely used with modern cutters, and an 



152 The Cincinnati Milling Machine Company 

ample supply of coolant for the cutter on that work which requires 

coolant : 

Cast Iron 

Spiral Mills 

Rough milling 65 to 75 feet 

Finish milling 80 to 120 feet 

Face Mills 

Rough milling 65 feet 

Finish milling 80 to 110 feet 

Machine Steel 
Spiral Mills 

Rough milling 70 to 75 feet 

Finish milling 100 to 140 feet 

Face Mills 

Rough milling 60 to 85 feet 

Finish milling 90 to 110 feet 

Tool Steel — Annealed 
Spiral Mills 

Rough milling 50 feet 

Finish milling 70 to 80 feet 

Chrome Nickel Steel (.30 to .40 carbon drop Forgings) 

Rough milling 45 feet 

Tobin Bronze 

Spiral Mills with Lubricant 

Rough milling 90 feet 

Finish milling 125 to 150 feet 

Brass 200 feet 

Aluminum 600 to 1,000 ft. 

Other Factors Which Determine the Life of the Cutter. 

The failure of the cutter is not always due to excessive speed. When 
the metal is gritty a grinding action takes place, which by and by 
dulls the cutter. This is especially true when cutting cast iron. 
For that reason special attention must be paid to the clearance 
angle of cutters, which will be taken up more in detail in the chapter 
on construction of Milling Cutters. 



A Treatise on Milling and Milling Maghines 153 





^■faB 



Fig. 143. Adjustable Inserted Tooth Slotting Cutter 

(Patent applied for) 

Then there is also the legitimate wear on the cutter caused by 
the edge rubbing over the work and the pressure of the chip against 
the teeth. This wear is not greater with fast than with slow speeds, 
but, if with slow speeds the cutter will be dulled in two days, with 
twice the speed it may become dulled in one day. The amount 
of work performed by the cutter will be the same for the same amount 
of wear, but the TIME required for doing it with fast speeds will be 
very much less than when slow speeds are used. 

For example: Assuming a piece of work that can be milled at 
100 rev., and that the feed per revolution should be .200". The 
resultant table travel will be 20 " per minute. Now, if we run the 
cutter 50 rev. and use the same feed rate, the table feed will be 10 " 
per minute, only one-half as fast as before. The cutter will be 
doing only one-half as much work and will last twice as long. 

On the other hand, if we feed 10" per minute at 50 revolutions 
and then increase the speed to 100 revolutions, but do not increase 
the feed, production will not be increased and the cutter will, theo- 
retically, last only half as long when milling the same number of 
pieces, because the cutter makes twice as many chips and therefore 
comes in contact with the work twice as often since the chips are 
only half as big as before. Some data confirming this are given in 
the next paragraph. Increasing the speed alone does not 

INCREASE PRODUCTION. 

Life of Cutters When Milling Cast Iron. Some very valu- 
able experiments were made by the Cincinnati Milling Machine 
Company on the effect of cutting lubricant on the life of the cutter 
when milling cast iron. The result of these tests is shown in the 
accompanying table. The cast iron bar milled was in each case 



154 



The Cincinnati Milling Machine Company 



36" long. All cuts were taken on scale. The cutter used was our 
standard slotting cutter, but with only one tooth operating, all the 
other teeth having been removed. 

Cutter — 5" diameter, %* face. Arbor — l^". 

Speed of cutter — 72 r. p. m. Cut — ^" deep, %" wide. 



Effects of Use of Lubricant and the Size of Chip on the Life 
of a Cutter Milling Cast Iron 









Total 


Total 


Wear 






No. 


Feed 


Feed 


Distance 


Wear of 


of Tooth 






of 


per 


per 


Traveled 


Tooth 


per 100" 


Remarks 


Cuts 


Min. 


Tooth 


per Sharp- 
ening 


(Radial) 


Traverse 






3-a 


.5 


.0069 


108" 


.0035 


.00324 


Lubricant. 


No Brace 


3-D 


.5 


.0069 


108" 


.003 


.00277 


Dry. 


No Brace 


3-c 


1.0625 


.0147 


108" 


.0035 


.00324 


Lubricant. 


No Brace 


3-d 


1.0625 


.0147 


108" 


.00325 


.0030 


Dry. 


No Brace 


3-e 


1 . 0625 


.0147 


108" 


.0015 


.00138 


Lubricant. 


With Brace 


3-f 


1.0625 


.0147 


108" 


.001 


.00092 


Dry. 


With Brace 


3-S 


.5 


.0069 


108" 


.00275 


.00254 


Lubricant. 


With Brace 


3-h 


.5 


.0069 


108" 


.003 


.00277 


Drv. 


With Brace 


6-i 


2.25 


.03125 


216" 


.0005 


.00023 


Dry. 


With Brace 


6-i 


2.25 


.03125 


216" 


.00025 


.000125 


Lubricant. 


With Brace 


6-m 


1.0625 


.0147 


236" 


.002 


.00084 


Dry. 


Braces 


6-n 


1.0625 


.0147 


236 


.00375 


.0015 


Lubricant. 


Braces 



The above tabulation shows some very interesting things. 
For instance, cuts a, b, c and d were taken with the outer end of 
the arbor supported from the overarm, but not tied to the knee 
with braces. This, therefore, allowed a slight amount of vibration, 
not sufficient to be noticeable, but it nevertheless existed and had 
its effect on the life of the cutting edge of the cutter. Comparing 
cut c for instance, with cut e, shows that with the braces, the wear 
on the cutting edge was not quite one-half as much as without 
braces. In the same way, comparing cut a with cut g, an improve- 
ment is again shown when the braces are used. 

We will consider here, only those cuts taken when the machine 
was equipped with braces. Let us first consider the effect of lubri- 
cant. Cuts e and f show that there was less wear when running 
dry, while cuts g and h show slightly in favor of lubricant. This 
is also true when we compare i and j. In the same way, comparing 
m and n, the result seems to indicate that it is better to run dry 
on cast iron. 



A Treatise on Milling and Milling Machines 155 

The conclusion to be drawn from all this is, that there is no 
advantage in using lubricant when milling cast iron, if we consider 
alone the question of the life of the cutter. However, it has been 
very clearly demonstrated that when milling frail pieces at a high 
speed rate, there is a decided advantage in using fast feeds and lubri- 
cant, when milling cast iron parts of this character, because of the 
cooling effect of the lubricant, which prevents the heating of the 
piece and in consequence, warping out of shape. It must be noted, 
however, that we do not recommend this, because whenever it has 
been tried on manufacturing operations it was found that the 
lubricant carried small particles of iron into the bearings of the 
machine, and caused such rapid deterioration that it was not 
practical to keep the machine in proper adjustment to do rapid, 
accurate work. 

Effect of Size of Chip on Life of Cutter. Even more interest- 
ing than the effect of lubricant is the effect of the size of the chip as 
shown by these figures. Comparing cuts e and g we find that with 
a feed of 1" the wear on the cutter is .00138, whereas when feeding 
Yi' the wear on the cutter is .00254 when the distance milled in 
each case is 108". In other words, feeding y^' per minute, the cutter 
came in contact with the work twice as often in milling a distance 
of 108", as it did when feeding 1" per minute, and the wear on the 
cutter was approximately twice as great. 

Again comparing cuts h and i. Cut i was taken with a feed 43^ 
times as fast as cut h, while the wear on the cutter at the slower 
feed per 100" of traverse was nearly 10 times as great as the wear 
on the cutter at the faster feed. 

These figures indicate quite clearly that the dulling of the cutter 
is in direct proportion to the number of contacts which the cutter- 
tooth makes with the work in a given length of travel. We believe 
that an entirely safe conclusion is that the wear per contact, that is 
to say, the wear per chip produced, is approximately the same for 
different sizes of chips when milling cast iron within the practical 
limits of milling. In other words, if we use a chip per tooth of .007", 
the cutter will make as many chips and in consequence will be 
dulled to the same extent when milling a piece 100" long as it will 
when taking a chip .014" thick, milling a piece twice the length, 
that is, a piece 200" long. All this shows the desirability of using 
the fastest feed that other conditions will permit. 



156 The Cincinnati Milling Machine Company 



CHAPTER VIII 

STREAM LUBRICATION 
CUTTER AND WORK COOLING 

It was found by experimenters that lubricant on a tool does 
something else besides producing a smooth surface. It also acts as a 
coolant and there has been a great deal of discussion as to whether 
the benefits are due to the fact that the fluid lubricates, or whether 
they result from its cooling effect. We will not consider here the 
action of the fluid as a lubricant, but only as a coolant. 

The limitation of the cutting speeds results from the fact that the 
act of cutting makes the extreme edge of the tool hot enough to 
draw its temper. Carbon steels lose their temper at a relatively 
low heat. High-speed steels differ from carbon steels in this respect 
only — that they can stand a much higher temperature before losing 
their temper. 

Generation of Heat by Cutting Tools. Most of the experi- 
ments above referred to were carried out on the lathe, and are 
briefly discussed in the preceding chapter. But what applies 
to a lathe does not necessarily apply to a milling machine. A 
lathe tool is constantly embedded in the work and the top of the 
lathe tool is constantly covered by the chip, so that the cutting edge 
of the tool, which is the part to be kept cool, receives very little, if 
any, of the lubricant, consequently it gradually accumulates heat, 
but it does not burn out because it also loses part of this heat. Finally 
a point is reached at which it loses heat about as fast as it receives 
it and, therefore, remains at an approximately constant temperature. 
When this temperature is the highest the tool will safely stand, 
then the speed, which produces this temperature, is the highest safe 
speed for that tool under the conditions assumed. 

A milling cutter works under entirely different conditions. A 
tooth enters the work, removes a chip and leaves the work, then 
travels through the air for the greater part of a revolution. It 
therefore has a better chance to dissipate the heat received than a 
lathe tool. But what is far more important, the fact that the cut- 
ter tooth is free of the work a large part of the time, gives an oppor- 



A Treatise on Milling and Milling Machines 157 

tunity to apply artificial means for carrying away the heat as fast 
as generated and thus keep the cutter cool at high speeds. 

The Cincinnati Milling Machine Company has carried on a 
long series of experiments to determine the most effective method 
of applying cutting lubricant and the extent to which speeds and, 
therefore, production, can be increased by the use of a sufficient 
volume of lubricant properly applied. 

It was found that the nature of the lubricant does not affect the 
cutting speed, provided the quantity is sufficient. It was further 
found that in the majority of cases the quality of finish is equally 
good with the cheaper compounds as with pure lard oil, when suf- 
ficiently large quantities of lubricant are used. 

The speed at which it is possible to run the cutter depends 
primarily upon the volume and method of application of the lubri- 
cant. The average small stream as usually provided, is by no 
means sufficient to secure ample cooling. After numerous trials 
we developed a system which deluges the cutter and work with 
lubricant, and as a result, we are able to greatly increase the speeds 
over those formerly attainable, and still keep cutters and work 
cool. 

These experiments formed the subject of an editorial in the 
"American Machinist/ ' by the editor, Mr. L. P. Alford. It appeared 
in the issue of April 16, 1914, and as it gives important data on the 
experiments as recorded by an impartial observer, the editorial is 
reproduced on the following pages. 

Editorial from the American Machinist, April 16, 191 U: 

"Progress in the art of cutting metals, as in all other lines of 
human endeavor, has been a slow advance with occasional sudden, 
pronounced jumps, followed by the same slow advance. One such 
jump came in 1900, with the announcement of the development of 
high-speed steel. This was first presented to the American Ma- 
chinists' readers in the issue of August 9, 1900. The feature was high 
speed. The editorial note said : 

The appearance of a large lathe turning a 17" steel shaft at this 
speed (150 feet per minute) is nothing less than startling. 

This article, I believe, is the announcement of the beginning 
of another jump in this curve of progress, at least as it affects multi- 
toothed cutting tools. The startling feature as in the case of high- 
speed steel, is the speed. Tests have shown peripheral cutter 



158 



The Cincinnati Milling Machine Company 



speeds and work feeds in steel, some eight to twelve times greater 
than those used in ordinary milling practice. 




Fig. 144 

Miller upon which high-speed milling tests were run. Cutter speeds 500 r. p. m.=458' per 
minute. Work feed 30^" per minute. Depth of cut Y% . Material, machinery steel, 0.2 carbon, 
0.5 manganese. 

The Cincinnati Milling Machine Company's Progressive 
Experiments. The conditions which have made these tests pos- 
sible are the direct result of the work that the Cincinnati Milling 




Fig. 145 

Chips removed by one cut across mild-steel block, 5 by 18", shown in Fig. 111. 

Machine Company, Cincinnati, Ohio, has done during the past six 
or eight years. In 1908 the American Machinist showed the line 



A Treatise on Milling and Milling Machines 159 



of Cincinnati High-Power Millers. Since that time this line has 
undergone progressive improvement, particularly in the selection 
of better materials. At the Pittsburgh meeting of the American 
Society of Mechanical Engineers in 1911, A. L. De Leeuw, until 
recently chief engineer of the company, presented a paper on Milling 
Cutters and Their Efficiency. A feature of this was data on the use 
of cutters with wide spaced teeth. This paper was abstracted on 
pages 753 and 787 of Vol. 35. 

Last year was shown this firm's Semi-automatic Miller, which 
was adapted for much higher cutting speeds and table feeds than 
were in common use for that general type of machine when it was 
designed. 

These developments set up the conditions of powerful, heavy 
machines, an extensive use of cutters with wide-spaced teeth, which 
permitted increased feeds, and experience with feeds and speeds 
somewhat higher than average practice. From this foundation 
experiments were begun with much higher work feeds and cutter 
speeds. The illustrations, Figs. 144 to 156, inclusive, show in 
graphic fashion some of 
the results. Details of the 
system have been made 
the subject of patents. 

To show what these 
results are, I can do no 
better than to give the 
records of the tests that 
I have witnessed. The 
machine upon which the 
high-speed tests were run 
is shown in Fig. 144. This 
is a No. 5 High-Power 
Cincinnati Miller driven 
by an independent motor, 
with a speed of the con- 
stant-speed pulley 50 per- 
cent greater than that for 
which the machine was 
designed. The steel cut was a mild machinery steel, 0.2 carbon, 
0.5 manganese, having an ultimate tensile strength of from 55,000 
to 65,000 pounds per square inch. The cutters were all of high- 
speed steel. 




Fig. 146. Stream Lubrication 

High-Power Miller showing hood, container and drainage 



pipe. 



160 



The Cincinnati Milling Machine Company 



Test No. 1. Cutter, spiral mill, 25° angle, 2>y 2 " diameter, 
9 teeth, 10° rake, 6" long. Arbor iy 2 " diameter. Depth of cut y % \ 
width 5", length 18". Speed of cutter 500 r. p. m., peripheral speed 
458 feet per minute. Feed 303^" per minute. Finish good for com- 
mercial milling where surfaces are to be bolted together. 

Test No. 2. All conditions the same as for Test No. 1, except 
that the depth of cut was reduced to 0.02", and the feed to 7. 23" per 
minute. The finish in this case was good enough to polish. 

Test No. 3. Cutter, a helical mill Zy 2 " diameter, 6" long, 3 teeth, 
angle with axis 69°, rake 15°, arbor iy, cutter speed 510 r. p. m., 

,-*— i peripheral speed 470 feet 

per minute, feed 303/2" per 

1 j_ 4 ^ § minute. Two cuts were 

taken, the first with a depth 
rg", the second with a depth 




of 



3 // 
16 • 



Test No. 4. A slotting 
cutter with sharp-cornered 
teeth 1" wide, 6^" diameter, 
rake 15°, 16 teeth, arbor 
V/i". Alternate teeth slope 
in opposite directions with 
the axis of the cutter. Cut- 
ter speed 510 r. p. m., pe- 
ripheral speed 835 feet per 
minute, feed 303^" per min- 
ute. Cuts were taken at a 
depth of A" and K". The 
finish was a good commer- 
cial finish in each case. 

Test No. 5. High-feed 
test, gashing with a gear cutter. Cutter 7 diametral pitch with extra 
hub, 12 teeth, 33/£" diameter, 10° rake, arbor Vy± r diameter. Cutter 
speed 218 r. p. m., peripheral speed 200 feet per minute, feed 112" 
(9}4 feet) per minute. Material of the same composition as for the 
blocks in the preceding test, in the form of a cylinder 1834" long and 
of a diameter representing a 30-tooth, 7-pitch gear. The machine 
upon which this test was made was a 28" Cincinnati Semi-automatic 
Miller. Repeated cuts were taken without any signs of distress of 
machine or cutter. 



Fig. 147 

Stream lubrication on Semi-automatic Miller; 
lifted away from cutter to show construction. 



hood 



A Treatise on Milling and Milling Machines 161 



Test No. 6. A feature of all the preceding tests was a copious 
supply of lubricant to carry off all the heat. In each case as soon as 
the cut was finished, cutter and work were felt and neither showed 
an appreciable rise in temperature. 

To show the effect of cutting dry the block and cutter of Test 
No. 1 were replaced and a cut started with a depth of J^"> feed at 
20" per minute, and a cutter speed of 87 r. p. m., peripheral speed 





Fig. 148. V/z' Diameter Mill 

Cut speed 77 r. p. m. Cut Y% deep per 5* 
wide. Feed 17!%* per minute. 65,000 lbs. tensile 
strength steel. 



Fig. 149. Helical Cutter 

%y<L diameter, 6" wide, feed 16" per minute. 
Material, 65,000 lbs. tensile strength steel; 
speed, 72 r. p. m. 



80 feet per minute. This cut was started dry and the cutter showed 
distress after running about 2^"; it was stopped, and the edges 
of the teeth were found to be blued. 

As a comment on the length of life of some of the cutters working 
under these conditions, a record is given of a cutter of the same 
description as the one used in Test No. 5, run to destruction. It 
milled 6,700", not including the cutter approach. This is equivalent 
to completely cutting 223 gears, 1" face, 7 pitch, 30 teeth. The 
cutter began to show distress at about the fourth cut from the last, 
and from this point to destruction the breakdown was rapid. Dis- 
counting these last three or four cuts, the cutter milled the equivalent 
of 220 gears of the dimensions specified. 



162 



The Cincinnati Milling Machine Company 



Stream Lubrication. The copious use or deluging of cutter and 
work with a lubricant or coolant has been mentioned. This is 
arranged for on Knee and Column Type Machines, as shown in Figs. 
144 and 146. Around the miller table is placed a light steel frame 
to confine the liquid. In the base is set a centrifugal pump capable 
of delivering 12 gallons per minute. This is some 10 times the 
quantity delivered by the geared pumps ordinarily used. The 
reservoir capacity is large, and in this the pump is submerged so 



f#j 


Ml 


*^ 


a. i 


m^ 


y 


~4 




JiS 


887 




Fig. 151. Semiautomatic Miller 

Machinery steel cutter standard slotting : ; 
■with sharp corners h" diameter, 325' cutting 
speed. Feed 112' per minute. 



Fig. 150 

Materia] 65,000-lb. machinery steel, 7 pitch 
gashing cutter, 12 teeth. Cut full depth of tooth. 
Speed 218 r. p. m. Cutter 3Jg* diameter. Feed 
112" per minute. 

that there is no suction piping or necessity for priming. The large 
capacity provides enough fluid so that an appreciable accumulation 
of heat is avoided. In addition, the surface of the table over which 
the lubricant spreads in a wide sheet acts as a means of cooling. 
The pump discharge under considerable pressure passes through a 
flexible hose to the cutter, or cutter hood, having in the line a large, 
quick-acting gate valve. From the table a large flexible steel tube 
returns the lubricant to the machine base. 

The preferable means of distributing the lubricant to the cutter 
is by means of a special cutter hood. This is shown in Figs. 146, 
147, 150 and 151. It completely surrounds the cutter. 

The advantages of the hood are principally three. It confines 
the large flow of lubricant directly to the cutter and work, thus 
securing an inverted bath or flowing stream and making all of the 



A Treatise on Milling and Milling Machines 163 

lubricant do its share in cooling. It washes the chips from the 
teeth of the cutter so that they can not be carried back into the cut, 
thus clogging it, dulling the cutter and marring the finished surface. 
It prevents the splashing of lubricant when used in large quantity. 
Incidentally, it is also a milling cutter guard, guarding against 
accidental injury to the operator. 

Effects of Stream Lubrication and High Speeds. It is 
instructive to consider in brief fashion the possible effect of these 
high speeds and lubrication upon the various limiting factors that 
enter into milling machine practice. 

Power of machine: Increased speed in milling means a slightly 
increased power consumption per cubic inch of metal removed. 
Tests made by the Cincinnati Milling Machine Company indicate 
that an increase of 100 percent in speed means an increase of about 
10 percent in power consumption per cubic inch of metal removed. 
Thus increased speed means more powerful machines. 

Ability of the cutter to remove metal : The ability of a cutter to 
cut is increased with an increase of speed, the feed per minute 
remaining unchanged, for the reason that the chip taken by each 
tooth is decreased. This means a decrease of strain, wear and heating 
effect. The total or final heating effect is increased, but this can be 
counteracted by copious lubrication. 

Size of arbor and its spring: The size of the arbor is one of the 
limitations in present milling practice, being governed by the sizes 
of commercial cutters. The feed per minute is a measure of the 
strain on the arbor; thus an increase of speed, giving a lessened 
pressure per tooth, reduces the arbor strain and tends to do away 
with the limitation of arbor size. To illustrate, if a given set of 
conditions permit of a feed of 2" per minute, then by maintaining 
this rate per revolution, but multiplying the revolutions per minute 
by 10, we get a permissible feed of 20" per minute with the same 
arbor stress. 

Heating of the cutter: The heating of the cutter is often THE 
limitation. This can be removed by using a quantity of lubricant 
or coolant sufficient to remove the heat as soon as it is released and 
keep cutter and work cool. 

Wear of the cutter: The wear of a milling cutter is dependent 
upon the number of linear inches milled if the depth of cut and feed 
per revolution are kept constant. Thus, increase of speed increases 
wear per unit of time. When the speed is sufficiently high so that 
by the aid of copious lubrication the chips are completely washed 



164 



The Cincinnati Milling Machine Company 



away, wear is somewhat reduced by avoiding the grinding action 
due to the cutting up of chips. 

Breakage of cutters: Frail cutters are a limitation in milling 
practice, because only a certain maximum feed per revolution can 
be taken, dependent upon their strength. If this feed is kept con- 
stant, production is increased directly as the speed is increased, 
without increasing the cutter strain or danger of breaking. 





Fig. 152. Milling Clutch Teeth 

Using a 27-tooth cutter, 3" diameter. 
191 r. p. m. Feed 112' per minute. 



Speed 



Fig. 153. Manganese Steel Rail 
Cut H* wide. iy s ' deep. Feed 3H' per minute. 



Heating of work: Uneven local heating when milling produces 
surfaces that are not flat because swelled portions are cut away. 
This is a progressive action as the cut advances, for the total heat- 
ing increases. Further, some work springs after removal from the 
fixture, due to its temperature when removed. The absence of 
heating will do away with this limitation. 

Spring of the work: A weakness and frailty of the work is 
another limitation, which is minimized for the same reasons brought 
out under "Breakage of cutters" above. 

Spring of the fixture: The analysis given for "Breakage of 
cutters' ' applies here. In many cases we might get greater production 
if the time for putting work into and removing it from fixtures could 



A Treatise on Milling and Milling Machines 165 

be reduced. However, the frailty of fixture or work prevents the 
use of quick-acting clamping devices, as eccentrics, cams, levers 
and the like. Thus, if the pressure per tooth in cutting is reduced, 
the pressure required for holding may be reduced, and clamping 
devices may be made to operate more quickly. Thus the influence 
of speed in this respect should be to increase production. 

Spring in the machine: The arguments presented under "Spring 
in the fixture" apply here. 

Distance of revolution marks on the work: It is claimed that 
output today is controlled in perhaps 90 percent of cases by the 
distance between revolution marks. Polishing or some following 
operation limits this distance. These marks must be near together, 
or the following operation can not be properly performed. An 
increase of speed with unchanged feed, bringing these marks closer 
together, is one obvious remedy. 

Smoothness of cut: One feature in high-speed milling is the 
throwing away of the chips, which resembles nothing so much as 
the throwing off of shavings and chips in planing wood. This 
complete removal of the chips, both by the effects of speed and 
copious flooding with lubricant, does away with the grinding effect 
on the finished surface. Thus, with a fixed distance between revolu- 
tion marks, high speed tends to give a smoother surface. It is 
possible that the flywheel effect of the rapidly rotating parts con- 
nected to the arbor influences this action. 

Cleaning fixtures and work: The washing effect of the lubricant 
on the work and fixture, when the lubricant is used in great quantity 
and under considerable pressure, may aid in increasing production. 

Chips from High-Speed Milling. The illustrations, Figs. 154, 
155, 156, show chips from high-speed milling, and the notes below 
indicate the conditions under which each was produced. 

Fig. 154. (A) From machinery steel, cutter spiral mill 3%' 
diameter by 6" long, 13^" arbor. Cut 5" wide, y% deep, cutter 
speed 500 r. p. m., feed 303^" per minute. Stream lubricated. 

(B) Conditions as for A except depth of cut ye". 

(C) From machinery steel, cutter helical mill 33^" diameter, 
6" long, 3 teeth, iy arbor, cut 5" wide, ye" deep. Cutter speed 
500 r. p. m., feed 30^" per minute, stream lubricated. 

(D) Conditions as for C except depth of cut }/%'. 

Fig. 155. (E) Conditions as for C except depth of cut ^", 
cutter speed 86 r. p. m., feed 20" per minute. 



166 



The Cincinnati Milling Machine Company 



(F) From machinery 
steel, keyway cutter, 6^" 
diameter, V face, V/^ ar- 
bor, cut a slot 1" wide, ^" 
deep. Cutter speed 500 r. 
p. m., feed 303^" per min- 
ute. Stream lubricated. 

(G) Conditions as for F, 
except depth of cut \£' . 

Fig. 156. (H) From ma- 
chinery steel, 7-pitch spur 
gear cutter, 4" diameter, 
cutting full depth. Cutter 
speed 220 r. p. m., feed 112 
per minute. Stream lubri- 
cated. 

(I) Conditions as for A 
except depth of cut jV, 
cutter speed 86 r. p. m., feed 
20" per minute. Stream 
lubricated. The removal 
of metal was at the rate of 
31 cubic inches per minute. 

(J) Conditions as for I 
except that the cut was 
made dry. It ran for only 
about 23^" when the cutter 
showed signs of distress. 
These chips were colored 
dark blues and purples in 
contrast to all of the other 
chips, which were bright 
and without any discolora- 
tions. 

The differences of all 
these chips from ordinary 
chips are evident. One fea- 
ture of these chips is that 
when they are produced 




Fig. 154 



A Treatise on Milling and Milling Machines 167 




F 






WMWWWWW\ { ^\ ] W^WWW 



T 



2 '3 



5 6 



7 



with sufficient lubricant 
they are entirely devoid of 
color. Here is one of the 
radical differences between 
high-speed milling and high- 
speed turning. In the origin- 
al article in the American 
Machinist, describing the 
announcement of high-speed 
steel, occurs this sentence: 

'The chips themselves left 
the tools at a temperature 
which drew them to beauti- 
ful blues and purples; this 
coloring of the chips is a 
practical shop test of the 
correct speed of the work.' 

In contrast, the absence 
of color in high-speed mill- 
ing chips is a practical shop 
test of the practicability of 
the feed and speed in use. 

Kinds of Lubricant. 
These tests seem to show 
that the nature of the lubri- 
cant does not affect the cut- 
ting speed provided the 
quantity is sufficient. That 
is, the principal action is one 
of cooling, and with even 
the cheapest cutting com- 
pounds there is sufficient 
lubricating effect, provided 
the quantity used is great 
enough to produce the 
necessary cooling." 

The Pump. The pump 
is of the centrifugal type 
and is capable of delivering 



Fig. 155 



168 



The Cincinnati Milling Machine Company 



from 12 to 15 gallons of 
lubricant per minute. This 
is many times the quantity 
delivered by the geared 
pumps used on milling 
machines at the time these 
experiments were con- 
ducted. This pump is lo- 
cated in a large reservoir in 
the base of the machine, 
and is completely sub- 
merged, therefore needing 
no suction pipe or priming. 
This large reservoir is 
necessary so as to provide 
a large enough body of 
lubricant to prevent it 
from accumulating an ap- 
preciable amount of heat. 
In addition, the lubricant 
spreads itself in a wide 
sheet over the table of the 
Milling Machine, and is 
thus aircooled before it re- 
turns to the reservoir. 

The supply is carried 
through a line of %" piping 
to a large quick-acting 
gate valve, by which the 
volume is regulated, 
thence through a flexible 
hose and down pipe to the 
cutter hood. This down 
pipe is clamped to the 
overarm and may be firm- 
ly secured in any desired 
position. 

The Cutter Hood. 
This cutter hood (pa- 
tented) is attached to the 



$"**J> 



v^.'V 









1 

*- ^ 



H 








EOT 



iTTimnmi 



2 3 






6 



7 



Fig. 156 



A Treatise on Milling and Milling Machines 169 

delivery pipe and partly encloses the cutter. The functions of 
the hood are: 

1. To confine the large flow of lubricant directly to the cutter 
and work, thus securing an inverted bath, and making all the lubri- 
cant take part in the cooling of the cutter. 

2. To wash the chips from the teeth so that they can not be 
carried back into the cut, causing the cut to become clogged and the 
cutter to be dulled. 

3. To prevent splashing of lubricant. 

A drain table (patented) consisting of a light steel frame is pro- 
vided to confine the lubricant to the table. This drain table is 
provided with a strainer of large area, and is so designed that a 
tight fit to the table is not required. 

A flexible metal return tube of ample capacity is provided to 
return the lubricant to the reservoir. 

This cutter and work-cooling system can be applied to all sizes 
of Cincinnati Constant Speed Drive High-Power Millers, Plain and 
Vertical (but not Universal). It should be attached in our factory 
before the machine is shipped. 

The Standard Equipment includes: 

1 centrifugal pump 

1 set of %" piping, gate valves, flexible hose, etc. 

1 standard hood 

1 drain table 

1 flexible return tube 

The standard hoods furnished as part of the equipment are 
as follows: 

No. 2 Plain and No. 3 Standard Machines: Hood for spiral 
mill 3" diameter, 3" face, 1J£" hole. 

No. 3 Plain and No. 4 Standard Machines: Hood for spiral mill 
3K" diameter, 4" face, Vfi' hole. 

No. 4 and No. 5 Plain Machines: Hood for spiral mill 4" diame- 
ter, 6" face, 2" hole. 

For Vertical Machines and Automatic Milling Machines the 
hoods must be made up special to suit the cutters and work and can 
only be furnished when we have definite information. Sometimes 
work is of such a nature that the hood can not be used with a face 
or end mill. 

The practical value of being able to use faster speeds, with the 
resulting faster table travels, is clear. On a number of regular 



170 The Cincinnati Milling Machine Company 

milling operations in our manufacturing department, the increase 
in feed, because of the faster speeds with stream lubrication, averages 
125 ^ faster than the best previous practice. 

Light Cuts with Stream Lubrication. The very large ma- 
jority of all milling work allows only relatively light cuts. This is 
either because the cutter is of delicate construction or the arbor is 
small; or the piece itself is frail or of such a shape that it is not 
feasible to hold it rigidly in a fixture, or because heavy feeds would 
heat or spring the work too much; and finally, because the revolution 
marks may have to be close together in order to get a presentable 
finish. 

Running the cutter at very high speeds makes it possible to take 
light cuts at a high rate of feed per minute with the following advan- 
tages: 

The pressure on the work is light. 

The work does not spring. 

The spring in the arbor is reduced allowing the use of smaller 
arbors and smaller cutters. 

Lighter fixtures can be used. 

Irregular pieces can be held in fixtures with less danger of being 
pulled out. 

The pressure between cutter and work being slight, there is not 
the danger of springing the arbor and consequently the finish is 
better, and the piece is finished to closer accuracy as to size. 

There is no heating of the piece, and in many instances it is 
possible to finish a piece with one cut, where heretofore two cuts 
were required. 

Heavy Cuts with Stream Lubrication. Xot only is this 
large flow of lubricant very beneficial on light cuts, but it also makes 
it possible to take the heavier cuts at very much higher cutting 
speeds, thereby permitting a smaller cut per tooth, thus reducing 
the strains on work and arbor. The volume of lubricant also car- 
ries away most of the chips, thus reducing the necessary cleaning 
of the jig to a minimum. 



A Treatise on Milling and Milling Machines 171 



CHAPTER IX 
MILLING CUTTERS 

In Chapter V, milling cutters and the fundamental principles 
of their action were discussed, but without going into the details 
of cutter construction. In this chapter we will discuss the design 
of cutters in detail. We will first consider the simple case of 
ordinary milling cutters. 

An ordinary milling cutter is a cylindrical body of steel with a 
hole through the center and with teeth running parallel or at some 
angle with the axis. If the teeth are parallel with the axis, the cutter 
is called a plain mill, and if they are at an angle, the cutter is called 
a spiral mill. 

When cutters are of relatively small size, they are made of a 
solid piece of steel. When of sufficiently large size, the body and 
teeth are separate and the cutters are then called inserted tooth 
mills. 

Solid Mills. The most important things about the body of the 
mill are the material of which it is made, and the thickness of the 
metal between the keyway and the bottom of the teeth. The metal 
is either carbon tool steel or high-speed steel. Carbon steel cutters 
are used less and less nowadays, but stream lubrication, discussed 
in the preceding chapter, makes it possible to use them to better 
advantage than before. Carbon steel cutters are often used for 
finishing operations on extremely exacting work, while high-speed 
steel cutters are used for roughing. Carbon steel acquires a finer 
edge than high-speed steel. This latter material is more or less 
brittle and the edges of a high-speed steel cutter under the mag- 
nifying glass sometimes show small serrations, which affect the 
quality of the finished surface when an extremely fine surface is 
to be produced. 

The end surfaces of the body of the cutter should be as nearly 
flat, parallel and at right angles to the axis of the bore as it is possible 
to make them. The result of defective ends of the cutter is that the 
arbor will be sprung when arbor collars and cutters are clamped 



i:: 



.hi Cincinnati Billing Machine Company 



together by the nut at the end of the arbor; the cutter will not 
run true, and the effect is the same as if one tooth were considerably 
higher than the others. This one tooth, therefore, does much more 







^-rmrrOMeo XTS-fr/try. 






A. modern sp iral 



Fig. 157 

■with wide spaced undercut teeth.. 



work than the others and dulls before the other teeth are affected. 
In other words, the cutter must be resharpened much sooner than 
if all the teeth were doing their share of the work. 



5TD KEY WAY 




ALL CUTTEI 



Fig. 158 



One of the earHer spiral mills with nicked teeth, having radial 
a. Tinas style of ratter has been superseded by the one shown 

im Fig- 124. 

The bore of the cutter should be true to size and perfectly round. 
As a role, the bore is partly relieved as is shown in Fig. 157. This 
relief is not provided when the cotter is short. 



A Treatise on Milling and Milling Machines 173 




FormRei 



ZMT 



^-^ 



3a 
Chip Breaker 

EnlBRGEO 

Fig. 159 



When milling cutters were first invented they were made with 
a very large number of teeth. The cutter was merely a rotating file, 
but as such, was a great improvement over a hand-operated file. 
Gradually the number of teeth was diminished, but it was soon 
found that if the teeth were relatively far apart, each tooth would 

have to take a fairly heavy chip. At that time 
cutters were either not ground at all, or ground 
by hand, and, of course, this made it impossi- 
ble to have the teeth on an approximately 
uniform diameter. Under these conditions 
some teeth would not cut at all and others 
would have to take twice or three times their 
legitimate share of the work, or maybe more. 
Not until cutter grinding machines were regularly used for sharpen- 
ing cutters, was it possible to use the milling cutter for reasonably 
heavy work. 

Faults of Cutters with Too Many Teeth. Until quite 
recently, teeth of plain mills and spiral mills were spaced about 
y%" apart, and even now cutters may be found in use on which 
the teeth are even closer together. These teeth were made with 
Radial Faces as in Fig. 158, so that their action was as shown in Fig. 
121. The tooth was forced into the metal, causing spring in the 
arbor, or in the work. Imagine a cutter cutting steel at a speed of 
70 feet per minute with teeth spaced %" apart, then 2,240 teeth will 
work every minute, and if we further imagine that the feed is 2" per 
minute, then each tooth 
takes a chip of which 
the greatest thickness is 
ttVtf of an inch, or less 
than one thousandth of 
an inch. It will be readi- 
ly seen that this chip is 
so thin that, as a rule, 
the tooth will refuse to 
bite into the metal, thus 
leaving a chip of double 
thickness for the next 
tooth. This tooth is perfectly capable of taking this double chip, 
but it is compelled to do this extra work because of spring in the 
arbor. In other words, something which is wrong must happen first 
before the cutter will cut at all. 




NEGATIVE 
ClERRRNCE 



Fig. 160 



174 



The Cincinnati Milling Machine Company 



Correct Design of Spiral Mills. A few years ago The Cincin- 
nati Milling Machine Company carried through a series of experi- 
ments as to the best spacing of the teeth of milling cutters. It was 
found that a much wider spacing than was then customary would 
give very much better results, and from these experiments a set qf 
dimensions for various styles of cutters was developed. Fig. 157 
shows our latest design of Spiral Mill, 4J/£" in diameter. This mill 

has 10 teeth correspond- 
ing to a spacing of about 
1.4*. At first we followed 
usual practice with an 
angle of spiral of about 
10° or 12°, but this was 
soon increased until now 
this angle is made 25°, 
unless there should be 
end teeth, as in end mills, 
when the angle is kept 
down to 20°. The faces 
of the teeth are not made 
radial, but are undercut; 
The amount of this rake 
this is the way the cutter 




Fig. 161 



in other words, 
should be about 



THEY HAVE RAKE. 

15° for steel, and tnis is 
should be made if used for steel only, but as a standard cutter may 
be used for either steel or cast iron, this rake angle is kept down 
to 10°. Due to this undercut the section of the tooth would be 
materially weakened, and for this reason the back of the tooth is 
milled with a double angle as clearly shown in the illustration. 
This actually gives a stronger tooth than on the older mills made 
without rake. The bottom of the tooth is made with a large fillet, 
for two reasons: In the first place, this fillet strengthens the tooth, 
and in the second place, it prevents chips from lodging between the 
teeth. 

It was found quite early in the investigation of milling cutters 
that a long cutter, that is, one with wide face, would cause con- 
siderable spring and chatter, and that this condition might be 
partly remedied by making nicks in the teeth, Fig. 158, thus cutting 
down the length of the chip. These nicks, or chipbreakers, have 
long been a regular feature of milling cutters. However, it was also 
found that a milling cutter with chipbreakers would not produce as 
fine a finish as one without them, so that quite often an additional 



A Treatise on Milling and Milling Machines 175 



cutter without chipbreakers had to be used for finishing. An 
analysis of this condition showed that this rough finish was due to 
the fact that one side of the chipbreaker had negative clearance. 
Fig. 160 will show this clearly. This side of the chipbreaker, there- 
fore, could not cut, but was dragged over the metal, and this pro- 
duced a torn finish, and besides, this point of the chipbreaker became 
the weak point of the cutter; in other words, it was the starting 
point for the breaking down of the cutter when at work. To over- 
come this, chipbreakers were made as shown in Fig. 161. They were 
produced by milling two notches crossing each other at the front 
edge of the tooth. The same result was obtained later on by con- 
structing the chipbreaker as shown in Fig. 159. These chipbreakers 
were necessary when the angle of spiral was 10° or 12° and were 
kept until this angle was gradually increased to 25°. The chip- 
breakers with clearance on both sides do not produce the torn 
finish caused by the ordinary kind of chipbreakers, so that the same 
style of cutter can be used for roughing and finishing cuts. How- 
ever, the corner of the chipbreaker still remains the weak point of 
the cutter and begins to 
dull first. It was also 
found that the edge of the 
tooth following dulled 
faster immediately be- 
hind each chipbreaker 
than the other parts of 
the cutting edge. All 
this goes to show the de- 
sirability of doing away 
with chipbreakers. 

Twenty-Five Degree 
Angle Spiral Mills. 

The angle of 25° is a 
great improvement over 
the old angle, for, with 
this angle no chip- 
breakers are needed, as will be clear from what follows. There 
is another reason why this angle of 25° is preferred. The wide 
spacing of the teeth allows one tooth of a 12° spiral mill to get entirely 
out of action before another tooth enters, and this causes more or 
less hammering. If the cut is deep, then this hammering is not 
noticeable, because one tooth is still in the cut when the next one 




Fig. 162 



176 



The Cincinnati Milling Machine Company 




enters, but when the cut is shallow the hammering becomes quite 
pronounced. The angle of 25 c does away with these conditions. 
Unless the cut is very shallow indeed, there will always be two 
teeth in action. Besides, with the 10 = or 12 c angle, the cutting 
action is not so free, and therefore the difference between chip and 
no chip means a great deal of difference in pressure exerted against 
the work and therefore a great deal of difference in the spring of the 
arbor. With the angle of 25 r the length of the tooth embedded in 
the work is never very great, and therefore the spring in the arbor 
is very much less and consequently the hammering is very much 
reduced. To illustrate this with figures, we shall assume a piece 
of work 4" wide and a cutter of 3 1 2 " in diameter, with nine teeth. 

We shall further assume that 
the depth of cut is }±* and 
; that the angle of the spiral is 
10" see Fig. 162 . The curve 
AB represents the path of the 
cutter in the work. Under the 
conditions given above, the 
angle AOB is 31 = 15 minutes. 
The angle between two ad- 
joining teeth. A OC. is 40 : , be- 
cause there are 9 teeth in the 
cutter, so that when a certain 
point of the tooth OA is just 
ready to leave the work, a 
corresponding point of the next tooth OC has not yet entered. 
It may be. however, that another point of OA still is in the 
work: in fact, this must be so. because the tooth is not parallel 
with the axis, but is cut with a spiral. This will be clear from 
Fig. 163. which shows a development of this cutter. Imagine a 
piece of paper wrapped around the cutter, the edges of the teeth 
having been painted with red lead and the piece of paper then taken 
of! the cutter and laid out flat. All the teeth will show on the paper 
as red lines. A x represents one of these lines. The angle which 
this line A x makes with a line AC at right angles with the edge of 
the paper is 10 \ The length of this line AC is 4", this being the 
width of the work. Of course it may be that the cutter is longer 
than 4". but we are only contemplating that portion of the cutter 
which is engaged with the work. From the dimensions of AC and the 
angle 10\, we find that A : C is .70532"'. In Fig. 162, A is just ready 




Fig. 16.3 



A Treatise on Milling and Milling Machines 177 

to leave the work, but the other extreme point of this tooth Aj has 
still 7 /io" to travel before it is in the same relative position. A 
simple calculation will show that the angle AOAi is 28° 30 minutes 
and, therefore, that the angle AjOC is 11° 30 minutes. We have 
found that any point of the cutter travels through the work through 
an angle of 31° 15 minutes, which is more than 11° 30 minutes, 
so that the point A x of the tooth OA is still in the work when the point 
C of the tooth OC enters. However, we see also that it is in the work 
for only a short time longer and, consequently, if the depth of cut 
were less than x /± the tooth OA would be completely out of the 
work before the tooth OC would enter. If, now, we should make 
the spiral angle 25° instead of 10°, we would have the same general 
conditions, but the actual figures would be changed. The angle 
AOB, Fig. 162, would still be 31° 15 minutes, but the line A X C, Fig. 
163, would now be 1.86524 " instead of .70532/ and the angle AOA x 
would now be 32° 15 minutes, so that the angle A x OC would be only 
7° 45 minutes. In other words, the tooth OC would be in action 
long before the tooth OA would leave the work and, consequently, 
the depth of cut might be very much less than 34" and yet there 
would be always at least one tooth in the cut. It will, of course, 
also be clear that the part of the tooth which first enters the work 
will be entirely clear again before the farther end of the same tooth 
enters, even in a cut 34" deep. In a shallower cut the section of 
tooth in engagement at one time will, of course, be less. This fact 
together with the free cutting action due to the shearing effect of 
the wide angle combine to produce a smoother action and the removal 
of more metal per horsepower than is possible with the older cutters. 

Results of Tests on Milling Cutters. The results of experi- 
ments on milling cutters referred to in the previous paragraph are 
summarized in the several test records printed below. Space does 
not permit of giving all the details here, but the data given will 
indicate quite clearly the great advantages possessed by cutters of 
the Cincinnati design. 

Three series of tests will be considered here, as follows: 

a. To show the influence of wide-spaced teeth. 

b. To show the influence of rake or undercut teeth. 

c. Tests on cutting capacity of face milling cutters. 

All of these cutting tests were made in a machinery steel bar 
having 55,000 pounds tensile strength, containing .20 carbon and .50 
manganese. Because of the great variation in the cutting qualities 



178 



The Cincinnati Milling Machine Company 



of different pieces of cast iron, it is difficult to formulate exact data, 
and the results published herein will therefore be confined to milling 
tests on uniform steel bars as above. 

Influence of Wide-Spaced Teeth. The tests given in table A 
were made with three spiral mills, all of which were 3" in diameter, 
with a l}i" hole, 25 c angle spiral, teeth ground with 5 C clearance, 
but with the faces of the teeth radial, that is, no undercut or rake. 
The cutters differed only in the spacing of the teeth. Cutter A had 
22 teeth, spacing about .43". Cutter B had 16 teeth, spacing about 
.59". Cutter C had 10 teeth, spacing about .94". The cuts were 
taken in a machinery steel bar 23 4 " wide, and the cuts were exactly 
the same depth in each case. 

Table A — Showing Influence of Wide Spaced Teeth 



Cutter 



A— 22 Teeth 



B— 16 Teeth 



Width of cut 2% 2% 2% 2h 2h 2% 



3 
16 



3 
16 



3 3 

16 16 

82 6S 



Depth of cut Y6 

Revolutions 80.4 i 

Actual feed in inches per minute. 11 . 70 

Cubic inches of metal removed 
per minute 5 . 94 7.63 9 . 52 6.14 

Amperes 60 70 74 

Volts 200 200 19S 

Actual h. p. at machine cor- 
rected for motor efficiency ... 13 . 44 15 . 75 16 . 5 

Cubic inches of metal removed 

by 1 h. p. in one minute 442 . 4S4 . 577 



67 



3 
16 



C— 10 Teeth 



2% 2% 2% 

3 3 3 

16 16 16 

69 63 6S 



14.8 IS. 46 11.9 15.11 IS. 6411. 9 15.11 IS. 77 



54 
196 



7.79 9.62 6.14 7.79 9 B8 

56 64 46 52 60 

19S 198 195 197 196 



11.77 12.32 14. 28 9 S4 11.39 13. 24 
.522 .631 .674 .625 .6S4 .731 



The above figures show very conclusively the advantage of wide 
spacing alone. Cutter B, for instance, removed an average of 21 c 7 
more metal than cutter A, and cutter C removed an average of i 
more metal than cutter A. 



. c 



Influence of Rake or Undercut Teeth. Tables B. C and D 
show the results of cutting tests made on a steel bar 5" wide, with 
cutters 3J/9" diameter, 6" face, used on an arbor IV diameter. 
Cutter A, Cincinnati Design Spiral Mill as in Fig. 157. 25 : spiral 
angle, 10 teeth, 1.11" spacing, with 10° undercut or rake. This is 
shown in operation in Fig. 164. 

Cutter B, a Cincinnati Design Cutter similar to the above, but 
with radial tooth faces, that is, without rake. This is shown in 
operation in Fig. 165. 

Cutter C, a Helical Mill as shown in Fig. 1S4. This is shown in 
operation in Fig. 166. 



A Treatise on Milling and Milling Machines 179 

All of these tests were made on a No. 5 Plain High-Power Cin- 
cinnati Miller, direct connected to a 35 h. p. motor and fitted with 
our stream lubrication system. The feeds and speeds as given in the 
tables are corrected for loss of speed in the motor and the horse- 
power delivered to the machine is corrected for motor efficiency. 




Fig. 164. Cutter A 

Spiral mill %y% diameter. 25° spiral. 10 teeth. 10° rake. 



Table B — Showing the Influence of Rake 

Cuts -is* deep. Machine set for 16* feed per minute. 



Cutter 



A— 25° Spiral 
10 Teeth 
10° Rake 



B— 25° 


Spiral 


10 


Teeth 


No 


Rake 


5 


3 




1 




65 


5 


14 


56 


13 


65 


86 


195 


18 


88 




724 



E— Helical Mill 



Width of cut 5 

Depth of cut ^ 

Revolutions 65 

Feed in inches per minute (actual) i 14.4 

Cubic inches of metal removed per minute. 13.5 

Amperes 56 

Volts 202 

Total h. p. at machine corrected for motor 

efficiency 12 . 58 

Cubic inches of metal removed by 1 h. p. 

at machine in one minute 1 . 074 



67.7 

15.04 

14.10 

6S 

198 

14.20 

.99 



180 



The Cincinnati Milling Machine Company 



Table B shows cuts that were taken ^ deep with the machine 
set at 16" feed per minute. The data obtained from the cuts with 
the helical mill are included in these tables as a matter of interest 
only. We are chiefly concerned with the relative value of cutter A 
with rake, and cutter B, which is similar to it, but has radial teeth. 
The figures show that the cutter with rake removed approximately 
48% more metal per horsepower minute than the cutter without 
rake. 




Fig. 165. Cutter B 
Spiral mill 3J^' diameter. 25° spiral. 10 teeth. No rake. 

Table C — Showing the Influence of Rake 

Cuts Y%' deep. Machine set for 16' feed per minute. 



Cutter 

Width of cut 

Depth of cut 

Revolutions 

Feed in inches per minute (actual) 

Cubic inches of metal removed per minute 

Amperes 

Volts 

Total h. p. at machine corrected for motor 

efficiency 

Cubic inches of metal removed by 1 h. p. at 

machine in one minute 



A— 25° Spiral 


B— 25° Spiral 




10 Teeth 


10 Teeth 


E— Helical Mill 


10° Rake 


No Rake 




5 


5 


5 


V% 


Va 


Vs 


65 


57.6 


62 


14.4 


12.8 


13.76 


27 


24 


25.8 


108 


172 


132 


196 


182 


190 


23.54 


23.60 


27.57 


1.15 


.715 


.935 



A Treatise on Milling and Milling Machines 181 

Table C shows similar tests but with cuts %" deep. Here it will 
be seen that the cutter with rake removed more metal per horse- 
power minute than in the previous case when taking a i^" cut. 
However, the cutter without rake did not do so well on the deeper 
cut. In fact, in this case, the cutter with rake removed approxi- 
mately 60% more metal than the one without rake. 




Fig. 166. Cutter C 
Helical mill V/<£ diameter. 66° helix angle. 3 teeth. 15° rake. 



Table D — Showing Influence of Rake 

Cuts %' deep. Machine set for 20' feed per minute. 



Cutter 



-25° Spiral 
10 Teeth 
10° Rake 



B— 25° Spiral 
10 Teeth 
No Rake 



E— Helical Mill 



Width of cut 

Depth of cut 

Revolutions 

Feed in inches per minute (actual) 

Cubic inches of metal removed per minute. 

Amperes 

Volts 

Total h. p. at machine corrected for motor 

efficiency 

Cubic inches of metal removed by 1 h. p. at 

machine in one minute 



62.6 

17.40 

32.62 

140 

192 

29.52 

1.10 



5 

% 

65 
11.25* 
21.09 

126 

193 

26.73 
.790 



89.6 
16.6 
31.12 

160 

190 

32.60 
.955 



♦This cutter without rake could not take this cut with the feed set for 20* per minute. 



1S2 



_:-:i : ^xsati Milling Machine Company 



I-rrd 1-rT I^illUTr. 



Te 
10* Hi 



e i-naiers a^aha. bu~ ~kh :he na:hhae 
Cliis comparison is not entirely fair, 
e could not be made to take the cot 

; rasa :'—■:. and The rrares riven in hais aab'.e There:' :re. ::::> 
if res-iias ibaahae:: arm :he airier ~ :rh rake ~i:h :he rnaiakie 
2i rer rihinie and The amer ^irhiar rake ~kh rhe aaa:hhie 
I- 1 :' r'eei rer aainnre. 

e resir.is :: raese r-sis are "err ikrinarnaiing. sh:~hai" seia- 
as Thev :::. The area: adTaj::azes: rrsi. ::' ~lde-5Ta:e-i reerh: 
.. rhe sTill zrearer aiTaniage ::' rake. 0: i-aarse i: nans: be 
in mind thai the iriinary ::rm of nicked tooth high-speed 
pira] rk~~. ~a::a is ::ns:dered sianiari ani rer/hi:i;~ ;;.:- 
: sni^a ::':.: r.:r surress.u..;:" raae sine :: rae :iii sh:*?rn 
tS h , _' ani 10. 

srs on Face Mills. The lesrs in aabie Z — ere iiaie ~i:a a 
.ah-?:~er Faie LIi_ as sa:"^rn ha Jig. 172. ai: rae :: :ianr ~as 
i ~i:a :ne :: v:i sianiari :h iimr. e: liiaienis. la These 
r:ier ::rre:ii:ns have beer, rraie :a z'eei ani sneei :•: :a.n- 
e ::r rhe .:ss ::' speed ha The ni:::r ani rae h:rsea :~er iehlrery 



: : r ra : 





Table E— Cu 


cring Tests 


on Face Mills 






irni£ ""hjhh 




Metal BemoTed 


_ Z _ '.— '.'. 


- " Total 


1 a _l z~ : 


-'-' 


- "' '"" lllirS 


— _ — 


-, r . _- . "_ ~L I't: 


H. P. iml 




~'~ -'-'- 




*" Mm. 


\firn 


'-:' 


- "- - L ^ " 


v 


1_ :: 11.52 


'-' 1 


-: 


1 : 4; - c 1 


51 


12.83 11.52 


^ 


-J 


1 : - - 4 if 


c _ 


12.83 11.62 


r'".' 


'-:' 


15 


5.81 


-:•-: 


1: :_ 14.52 


v: 


'-:' 


15 


5.81 


1; 


16.11 14 52 


r'V 


'--' 


15 


5.81 


:4 


15.82 14 52 


;-:- 


-.: 


I-:'-; 


" :: 


52 


:? :: 14 u 


1.082 


-i' 


l:i. 


7.63 


52 


13.10 14 30 


1.091 


w 


------- 


.-•: 


12.53 14.17 


-i' 


■-■-.-__ ' :■: 


:•: 


12.53 14.37 


--' 


:■:** 


7.63 


- " 


12.83 14.30 


1.114 


5 m 

- -: 


1: 


" 70 


~ 


:; 12.02 


1.103 


-: ' 

■ - 


:-: 


7.68 


ee 


12. 


1.101 


: ' 


: r l_ 


- i: 


-/-. 


11.16 11.92 


1069 



The above figures are comparative only in relation to the cubic 
inches removed per horsepower per minute with this miQ at dif- 
ferent depths of cut. They indicate that this mill showed its highest 

ehacieajj :a :a:s : . ieep. aai :aa: :here ~ai i. ie::ied rahha^ :h 
: :' effi : iea :y ^r.ih cuts Jf deep. 



A Treatise on Milling and Milling Machines 183 

Relation of Depth and Width of Cut and Feed to Efficiency. 

This relative efficiency applies to this cut only. At some other 
width of cut and some other feed the relative efficiencies of cuts of 
different depths will show different results. It must be remembered 
that the efficiency of the cutter, that is, the metal it will remove with 
one horsepower in one minute, depends on three factors: width 
of cut, depth of cut, rate of feed. As proof of this we need only call 
attention to extreme cases: 

1. An extremely wide cut. For instance, a cut in steel 10" 
wide, ^2" deep, will not prove efficient as compared with the above 
cut yq" x 5" at the same rate of feed, although the cut has the same 
area of section. 

2. An extremely deep cut. For instance, a saw -^" wide can 
not possibly take a cut 10" deep, although this will again have the 
same area of section. 

The above figures will prove very valuable when estimating the 
capacity of a Miller for a given piece of work, or when estimating 
production on a given piece of work to be done on any particular 
machine. While the above tests are confined to the use of spiral 
mills and face mills, they will indicate that similarly good results 
may be expected from end mills, side mills and other cutters when 
made in accordance with the Cincinnati design. (See Chapter IX, 
Power Required to Do Milling.) 

Some examples of these different styles of mills are shown on 
the following pages and will serve as a guide for anyone desiring 
to make his own milling cutters. However, we recommend that 
cutters always be bought from a reliable cutter maker. This 
is a special business and those who have made it a study and have a 
fully equipped plant and men experienced in this work can invari- 
ably furnish a better cutter than can be made in a shop that is not 
specially equipped for doing this work. Besides, when all the expense 
is figured in, the purchased cutter will be found to be cheaper. 
We do not make cutters ourselves, but will always gladly refer 
others to reliable concerns who make that their business. 

End Mills with Shank. Fig. 167 shows End Mills with taper 
shanks. It will be noticed that on these the angle of the spiral is 
20° instead of 25°. This is done because the spiral angle also 
becomes the rake angle of the end teeth. A 25° angle would be too 
great. At the same time it is desirable, for the reasons given above, 
to keep the spiral angle as wide as is practical. A compromise 



184 



The Cincinnati Milling Machine Company 



angle of 20° has proven satisfactory. It will be noticed that these 
end mills also have then- teeth undercut 10° and the faces of the 
end teeth are cut back of the radial line this same amount. With 
the older design these things would have been out of the question 
because the teeth would have become entirely too weak. The mills 
shown in the drawings have the backs of the teeth formed with 
double angles, giving them ample strength. 



20 Spiral 




Fig. 167 



It used to be the practice to continue the end teeth of an end 
mill down to the center, or at least as close to the center as it was 
possible to go. This served no purpose whatever. If the 2" end 
mill shown in Fig. 167 takes a cut, say, Y± deep, with y% feed per 



A Treatise on Milling and Milling Machines 185 

revolution, then each of the teeth will take a bite of ^4". It may seem 
that this is a very small cut for this size end mill, but at a speed of 
70 feet per minute the cutter will make 135 revolutions per minute, 
and as we have }/$" feed per revolution, the feed per minute will be 
16 y%". This illustration also shows that it is the peripheral teeth of 
the end mill and not the face or end teeth which do the cutting, and 
it further shows that only ^" of the edges of the face teeth come 
into play. 

In the end mill shown the body is counterbored. This is done 
mainly to provide for many regrindings. The corners of the teeth 
are rounded or beveled. These extreme corners, if made sharp, 
are the weak points of the cutter. A rounding or beveling of this 
corner adds much to the life of the cutter. 




CUTTERS-^ AND WIDER 

HAVE 12° SIDE CLEARANCE 

ON EACH SIDE 

10 



12 TEETH -H-S-S 



Fig. 168 



Side Mills. A modern Side Mill, 5" diameter, is shown in Fig. 
168. As practically all of the work done by a side milling cutter 
is done by the peripheral teeth, it is important that these teeth 
should be undercut. 

When side milling cutters are to be used for milling slots in 
which the periphery and both sides are in action, and if the correct 
width of the slot is known, then a cutter may be designed with rake 
in all directions by simply building the cutter out of two similar 



186 



The Cincinnati Milling Machine Company 



cutters placed side by side with the peripheral teeth cut spirally, 
one-half being right-hand and the other half being left-hand (see 
Fig. 169) . The cutter as shown is made in such a way that the proper 
width of cut can be maintained by placing spacers between the two 
halves. If the two halves of the cutter were flat where they join 
each other, then the spacing out would leave an opening between 
them and this would leave a ridge in the work. For this reason 
they are made interlocking and the teeth of one-half overlap those 




Fig. 169 

of the other. The construction as shown has another advantage, 
namely, that though the teeth are wide-spaced, there will be no 
hammer blow because the teeth of one-half are in action before 
those of the other half are out of action. 

Shell End Mills. Fig. 170 shows a 2>YJ Shell End Mill. Shell 
end mills are in all respects similar to the taper shank end mills, 
except that the angle of the spiral is 15° instead of 20°. This style of 
cutter is seldom used as a spiral mill. Its action is the same 
as that of face mills described later. These cutters are driven 
by shrinking them on to a short arbor, about .0005" larger 
in diameter than the standard size of the hole in the cutter. 
Placing the cutter in boiling water heats it sufficiently to 
let the arbor enter. In addition, the arbor is provided with a driv- 
ing key. 

Reference is made to the action of this style of cutter in Chapter 
V. The action is entirely different from that of a plain or spiral 



A Treatise on Milling and Milling Machines 187 

mill. The face mill makes a chip like that of a planer tool, the only 
difference being that the tooth of a face mill sweeps in a circular 
path, whereas the planer tool removes the chip along a straight 
line, the side of the tooth doing the cutting. 




VV%JY° 




SECTION A-B 



ROUND CORNERS 
SEE DETAIL - 

V " 




10 TEETH H.S.S 




BACK VIEW SHOWING LOCATION 
OF KEY SEAT IN RELATION TO 
TEETH 

ENLARGED DETAIL SHOWING MANNER 
OF ROUNDING CORNERS OF TEETH 

Fig. 170 



Face Mills. Fig. 171 shows a 9%" Cincinnati Standard Face Mill, 
and Fig. 172 the corresponding size of High-Power Face Mill. They 
are similar in most respects, the difference being that the High Power 
Face Mill is especially built for the heaviest kind of duty. Both styles 
consist of a body in which slots are milled for the insertion of the 
blades. These bodies are made of steel. The slots for the blades 
are milled in the body at an angle of 7° with the center line. The 
blades themselves are made out of rectangular stock, ground to a 
driving fit into these slots. The blades are held in place by pins 
which are flattened on one side, thus making a wedge as clearly 
shown in the illustration. This brings the backs of the blades up 
against solid metal, and the amount of this metal is sufficient to 
support the blades under the heaviest cuts. A heavier stock is 



188 



The Cincinnati Milling Machine Company 



ib-ij 




A Treatise on Milling and Milling Machines 189 

used for the blades of the High Power Face Mill than for those of the 
Standard Face Mill. Though the blades are driven in and held by 
the taper wedge, it is possible to take such heavy cuts that the 
blades will move endwise and it is for this reason that the High Power 




\<r 






<o«> 


i°;0 

ulOu. 






QO O 





Face Mill is provided with a backing-ring, which is bolted on to the 
body of the mill. This backing-ring holds screws supporting each 
blade individually. This arrangement also permits of setting the 
blades forward as wear takes place. 



190 



The Cincinnati Milling Machine Company 



Particular attention should be paid to the angles. The rake 
angle, that is, the angle which the face of the blade makes with 
the radial line is 15°. The clearance angle on the peripheral edge 
is 7°. That portion of the blade which has this clearance angle 
is only -g^" wide, and the blade is ground away at an angle of 25° 
back of this narrow land; that is, at 10° with the tangent at this 






A 


B 


c 


A/ii R 


3 

1 6 


.0987 


.0857 


f\/o2. 


1 

A- 


.1406 


.1093 


^V l 1 


' 5 

IS 


.1718 


.1406 


x*\(l 


3 


.2031 


.1718 




7 

16 


.2343 


.2031 


/ >T^r 


i 

2. 


.2657 


.2343 



ARRANGE KEYWAYSO 
TEETH ARE STAGGERD 



8 TEETH 



Fig. 173 

A 2Y>" diameter interlocked splining cutter. 



point. This is done mainly to avoid unnecessary grinding when 
regrinding the cutter. The face edges have a clearance of 10° and 
are ground away at an angle of 20°; that is, 13° with the body of 
the mill. The blades are set at an angle of 7°, with the axis 
of the mill, so as to provide some rake at the point where the face 
edge of the blade slides over the finished work. Though, theoretically 
speaking, this face edge does no cutting, in reality it does remove a 
small amount of metal which is left there due to the spring in the 
work, the fixture, or the machine. It should also be noticed that the 
face edge of the blade is not left straight, as it is in taper shank end 
mills. There is first a rounded corner with a ye" radius, then a 
flat part ye" wide, and then the rest of the face edge of the blade is 
ground away with an angle of 7 to 10°. As there are 16 blades in 
the 10" face mill, and as these blades are V/± wide, there would 
be 20" of cutting edge resting on the work if these blades were not 
ground back. If the width of the work is somewhat less than 10", 



A Treatise on Milling and Milling Machines 191 

somewhat less than 20" of blade would be resting upon it, but in 
either case this would have a tendency to chatter. 

Too much stress can not be laid on the necessity of making both 
the body of the cutter and the blades as heavy as it is practical to 
make them. We can only give here sufficient information to enable 
the toolmaker to comprehend the principles on which correct cutter 
design is based. Lack of space forbids us to go into detail and we 
will only show here a few additional examples of milling cutters 
with notes as to their principal features. 




Fig. 174 



Splining Cutters, Saws, Slotting Cutters, etc. Fig. 173 
shows a Splining Cutter made interlocking, and particular attention 
is called to the simple method of interlocking, the entire half of each 
part being made thinner than the other half. This design works 
well for cutters from -ft* face up. 

Fig. 174 shows a Saw arranged to be driven not only by the key, 
but also by two pins which are held in a flange keyed to the arbor. 

Fig. 175 shows a thin Slotting Cutter. These thin slotting cutters 
are quite capable of doing very rapid milling, except for the fact 
that the body is liable to break through the keyway, and even if 



192 



The Cincinnati Milling Machine Company 



they do not break, the small amount of bearing which the cutter 
has on the key is liable to indent the key, making it very difficult to 
remove the arbor collars. For this reason such narrow cutters 
should be made with hubs as shown. 



KEYWRY i6WIDf I 




. t 



29°34' 



side yew of 

TOOTH ENLRBGfO 



TOP VIEW OP TOOTH ENLRRGFD 

Fig. 175 




Fig. 176 



Fig. 176 is a Thread Milling Cutter. The particular screw 
to be cut has no finish except on the threaded portion, and the cutter 
is arranged in such a way that it turns up the outside while it mills 
the thread. This cutter, also, is provided with a hub. 

Fig. 177 shows another cutter provided with a hub, and which 
has some features that are worth noting. It will be seen 
that the teeth have alternate side rake in opposite directions, and 
further, that the teeth are not the full width of the cut to be taken. 
This arrangement allows the chips to come out freely, makes a very 
smooth side cut and prevents the chips from sticking in the cut. 
It often happens that when the chip is the full width of the cut the 
expansion of the chip wedges it in the cut and this causes not only 
excessive power consumption, but also more especially, a rough side 
finish. 

Fig. 178 shows a cutter of much the same peculiarities except 
that it has no side cutting teeth. Each tooth, however, is given 
side rake and the teeth are again relieved so as to prevent wedging 
of the chips. It will be observed that the relief consists of beveling 
the edge of each tooth alternately and is always found on the side 



A Treatise on Milling and Milling Machines 193 

of the tooth where there is no rake because it is the rake side only 
that is expected to do work. 

Formed Cutters. Fig. 179 shows a Form Relieved Cutter, for 
finishing parts to an exact outline. These cutters are sharpened by 
grinding the faces of the teeth, and they retain their original outline, 
providing the teeth are always ground radially and straight. Cutters 
for cutting the teeth in gears belong to this class. 

Fig. 180 shows a Gear Stocking Cutter on which the alternate 
teeth are provided with right and left-hand side rake, all teeth 
having 10° undercut. This cutter has proven extremely satis- 
factory for roughing out gears. 

Fig. 181 shows an inserted tooth End Mill made in one piece 
with the shank. In the smaller sizes this makes a stronger mill 
than when the body and shank are separate, since in that case 




Hill 
Teeth 



Bevet Each. 

fllTlHnRTE TbOTH 



KCtwAy^-g 



iHTESlDE 7T T~~qK ™ § 

RsShowm | . i /*-50-*\ I J 





top View Of TerniEriiRRGED- side view 

Fig. 177 




Fig. 178 



the end of the shank must be quite small in diameter because the 
body of the mill will not admit of a large bore. 

Fig. 182 shows an Angular End Mill made in one piece with the 
shank. 

Fig. 183 shows an Angular Milling Cutter for use on an arbor. 

Helical Mills. Fig. 184 shows what we call a Helical Cutter, 
because its most striking feature is that the teeth are formed in a 
helix around the body. This cutter has several peculiarities which 



194 



The Cincinnati Milling Machine Company 



make it capable of doing some work which can not be done with 
ordinary cutters, and which, on the other hand, limit its usefulness 
in other directions. This cutter is made as shown in the illustration 




Fig. 179 



as a single cutter, or sometimes as an interlocked cutter, right and 
left-hand. It might be supposed that the end thrust must be con- 



▼:c- s :■--- = %: 

V LEFT - = VC 




siderable with such a cutter, and for this reason the first cutters of 
this nature were made right and left. Tests have shown, however, 



A Treatise on Milling and Milling Machines 195 



32 "6 "2 ,' 6 LONG 



ENLARGED VIEW OF 
CORNER OP BLROE, 




'-*•« ".7*9 tS?! 

8 -TEETH *-itl rim 



A- . 

/TTolO* 

rH FIX J! 

3 JI • t ii=i-z3 



3 M 






3 «S 



Fig. 181 

An inserted tooth end mill with shank. 




Fig. 182 



196 



The Cincinnati Milling Machine Company 



that a cut which requires 80 amperes current with a right and left- 
hand cutter, requires 85 amperes with a single cutter, so that the 
end thrust amounts to only about 6% of the power required for the 
cut. 







Fig. 183 



The distinctive features of this cutter are that it cuts with a 
shearing cut; that it pushes the chips off sidewise; that it makes 
toothmarks, and not revolution marks; and that it does not spring 
away from the work. This latter property makes it especially 



SHOWN BY 
THIS TOOTH 




I CUTTER H.5.S. 3TE6TH 5^ LETRD- 1.833 PITCH. 66° SPIRP.U (nPPROXtMBTe) 

Fig. 184 

valuable for cuts on thin work. If, when a cut is in progress, the feed 
be stopped while the cutter still rotates in contact with the work, 
it will be found after the feed has been reengaged and the cut finished 
that no mark is left on the finished surface at that point where the 



A Treatise on Milling and Milling Machines 197 



feed temporarily ceased. The only indication of the stopping of 
the feed will be that a somewhat different gloss will be observed 
at that point. This property of the cutter makes it possible to 
start a cut by feeding the work upward and then changing the direc- 
tion of the feed, say, to 
the horizontal, without 
causing a depression where 
the change of direction 
took place. Thin plates, 
springy work, copper bars, 
test pieces of boiler steel, 
etc., have been very suc- 
cessfully milled with this 
cutter. 

An example of work 
that this cutter will do 
successfully, and which is 
practically impossible with 
any other equipment, is 
shown in Fig. 185. This 
consists of milling steel 
test bars to size, Fig. 186. 
As is well known, these 
bars must have an accurate section and the sides must be parallel, and 
to size. In the illustration shown a number of pieces were clamped 
together for convenience in holding. The total width of the cut 
was 4J4", the depth J4", and the feed 4^" per minute. 

The work is first fed vertically to the cutter, then the horizontal 
feed is thrown in, and the cut is taken the proper distance. Because 
of the free cutting action of this 
cutter the work can be fed first 
vertically, then stopped and fin- 
ally fed horizontally without leav- 
ing an offset, thus insuring bars of 
the same sectional area throughout 
the entire length, with sides paral- 
lel and accurate for size. 

Any other form of milling cutter will dig into the work and leave 
a groove in the work at the time when the vertical feed is stopped 
and before the table feed can be engaged. 

Another illustration of this cutter at work and one which also 




Fig. 185 



10 



-; — 



V 



548-L. 



Fig. 186 



198 



The Cincinnati Milling Machine Company 



shows the nature of the chip is shown in Fig. 166. An even more 
definite idea of their form may be obtained from the chips at D 
in Fig. 154, and at E in Fig. 155. 

Fig. 187 shows a modification of this cutter milling the steel 
Universal Joint Shafts for Cincinnati Milling Machines. These 
shafts are turned with a head, the diameter of the head being equal 
to the largest diameter seen in the illustration. The cross feed 




Fig. 187. No. 3 Vertical with Circular Attachment and Helical Mill 

Speed, 9i revolutions. Feed, 234' per minute. Time, per piece, 7 minutes. 

brings the cutter into proper depth; the longitudinal feed then is 
used, after which the circular feed forms the rounded end; the 
longitudinal feed is then used once more on the opposite side of the 
piece and this finishes the operation. 

Fig. 188 shows another modification of this Helical Mill as used 
for milling out the ends of connecting rods. A single hole is drilled, 
the cutter inserted and the table is fed first horizontally and then 
vertically so that the cutter, traversing a rectangular path, cuts the 
desired opening into the end of the rod. A final finishing cut then 
brings the opening to size and proper finish. Rods 5" thick have 
been successfully milled with a cutter 1%" diameter at a roughing 
feed of z /i" and a finishing feed of 3fJ' / per minute. 

Making Spiral Milling Cutters. The Milling Machine is 
shown set for making spiral cutters in Fig. 189. The table is swiveled 



A Treatise on Milling and Milling Machines 199 




NOTE' DO NOT WERKEN CUTTER BY NECKING OR IERVIN& 
B» . KSQURRE CORNERS 




Fig. 188 

to the proper angle and the Dividing Head is geared, all as given in 
the table, page 201. 

Setting the Cutter. The cutter should be set before the table 
is swiveled. Since spiral mills are always cut with a double angle 
cutter, Usually one that has a 12° angle on the side which forms the 




Fig. 189 

Taking one of the two cuts required when making a modern spiral mill. 



200 



The Cincinnati Milling Machine Company 



cutting face of the tooth, it is necessary to adjust the work oft 
center., so that when the cutter is the right height above the head 
centers to give us the proper depth of cut., a straight edge placed 
along the edge of the tooth on the 12 : side will line up with the 
dividing head center. This will give us radial teeth as shown in 
Fig. 190. 

However,, the new cutters with undercut faces and wide-spaced 
teeth require two cuts. The setting of the cutter in relation to the 
work is shown in Fig. 191. In this case it will be noticed that the 
work must be offset more than in the previous case. It should be 
offset so that a straight edge placed along the edge of the cutter on 
the 12" side will form an angle with a line drawn from the outside 
diameter of the work to the center of the headstock of 10 : for 10" 
undercut, and 15 c for 15 = undercut cutters. 

This leaves the tops of the teeth entirely too wide as at a. 
Fig. 191. A second cut is then taken to bring the teeth to proper 
form as at b and c. 





Fig. 190 



Fig. 191 



A Treatise on Milling and Milling Machines 201 



Leads, Change Gears and Angles for Making Spiral Milling Cutters 















Angle for 


Diameter 


Lead 


Gear 


1st 


2d 


Gear 


Setting 


of 


in 


on 


Intermedi- 


Intermedi- 


on 


Milling 


Cutter 


Inches 


Worm 


ate 
Gear 


ate 
Gear 


Screw 


Machine 
Table 


M 


3.24 


28 


48 


40 


72 


25% 


y* 


4.17 


40 


64 


48 


72 


25% 


*A 


4.68 


40 


64 


56 


72 


25% 


Vs 


6.12 


56 


40 


28 


64 


2414 


l 


6.67 


64 


56 


28 


48 


2514 


1M 


8.33 


48 


32 


40 


72 


25^ 


m 


10.29 


72 


40 


32 


56 


24% 


1% 


11.66 


56 


32 


48 


72 


25% 


2 


13.33 


64 


32 


48 


72 


25^ 


2% 


15.24 


64 


28 


48 


72 


25 


2V 2 


16.87 


72 


32 


48 


64 


25 


2% 


18.75 


72 


32 


40 


48 


25 


3 


19.69 


72 


32 


56 


64 


25^ 


3% 


21.43 


72 


28 


40 


48 


25^ 


VA 


23.33 


64 


48 


56 


32 


25% 


3% 


25.57 


100 


64 


72 


44 


24% 


4 


26.67 


64 


28 


56 


48 


25% 


4% 


28.67 


86 


48 


64 


40 


25 


VA 


30.71 


86 


32 


64 


56 


24% 


4% 


32.73 


72 


32 


64 


44 


24^ 


5 


32.73 


72 


32 


64 


44 


25% 


5% 


34.72 


100 


24 


40 


48 


253^ 


5A 


37.04 


100 


24 


64 


72 


25 


5% 


39.29 


100 


28 


44 


40 


24% 


6 


39.29 


100 


28 


44 


40 


25^ 



Leads, Change Gears and Angles for Making Spiral End Mills 















Angle for 


Diameter 


Lead 


Gear 


1st 


2d 


Gear 


Setting 


of 


in 


on 


Intermedi- 


Intermedi- 


for 


Milling 


Mill 


Inches 


Worm 


ate 


ate 


Screw 


Machine 


Inches 






Gear 


Gear 




Table 


% 


2.08 


24 


64 


40 


72 


20^ 


Vs 


3.24 


28 


48 


40 


72 


19% 


y 2 


4.17 


40 


64 


48 


72 


203^ 


V* 


5.44 


56 


40 


28 


72 


20 


% 


6.48 


40 


48 


56 


72 


20 


% 


7.41 


40 


48 


64 


72 


20% 


l 


8.33 


48 


32 


40 


72 


20^ 


v/% 


9.70 


64 


48 


32 


44 


20 


1% 


10.94 


56 


32 


40 


64 


20 


m 


11.84 


64 


24 


32 


72 


20 


VA 


13.12 


56 


32 


48 


64 


20 


1% 


15.24 


64 


28 


48 


72 


20 


2 


17.14 


72 


56 


64 


48 


20% 


2A 


19.59 


64 


28 


48 


56 


20 


2V 2 


21.43 


72 


28 


40 


48 


20% 


2A 


23.33 


64 


48 


56 


32 


20% 


3 


26.25 


72 


48 


56 


32 


19% 


3% 


28.00 


64 


40 


56 


32 


20 


3H 


30.86 


72 


28 


48 


40 


193^ 


3% 


31.50 


72 


40 


56 


32 


2oy 2 


4 


34.55 


86 


56 


72 


32 


20 



202 



I H i_ C ^NCINNATlMlLLING MACHINE COMPANY 




The No. Ik Cincinnati Universal Cutter 
and Tool Grinder 



(Patents Rights Fully Reserved) 



A Treatise on Milling and Milling Machines 203 



CHAPTER X 

GUTTER SHARPENING 

Exhaustive experiments made by The Cincinnati Milling Machine 
Company show that the clearance on the cutting edge of a cutter 
plays an important part in the output of the machine. No arbitrary 
clearance angles for given materials can be laid down because other 
conditions also influence the matter. It has been found by keeping 




Fig. 192 



a careful record that it is possible to decide on a correct clearance 
for a given piece of work which will increase production as much as 
50% over the best average practice. 

We can not emphasize too strongly the importance of not only 
sharp cutters, but properly sharpened cutters. Even a milling 
department which keeps its cutters sharp and does not employ 
proper clearance angles may fall as much as 20% short of the possi- 



204 



The Cincinnati Milling Machine Company 




Fig. 193 



ble output without realizing it, as there will probably be no indication 
of serious trouble. Cutters as sent out by the cuttermakers are 
ground to a standard clearance and usually have too much clearance 
for satisfactory operation. 
It is always best therefore, 
to sharpen a new cutter 
before putting it into use. 
In order to provide the 
means for keeping cutters 
as well as other tools, in 
properly sharpened con- 
dition, in the easiest and 
quickest way, a cutter grinding machine as shown on page 171 
should be used. Its application is indicated by the illustrations. 
Fig. 192 shows the setting preliminary to sharpening a spiral 

milling cutter. The 
cutter mounted on a 
mandrel and held be- 
tween centers in the 
usual way, is adjusted 
vertically to the proper 
height by raising the 
knee until the gauge A 
coincides with the line 
B on the column. This 
brings the center of the cutter in the same horizontal plane with the 
center of the emerywheel. The setting gauge is now placed in posi- 
tion so that its end E is immediately in front of the emerywheel 
and one tooth of the 
cutter is brought to 
the gauge, which also 
brings it in the same 
horizontal plane with 
the center of the cutter 
and the emerywheel 
head. The gauge is 
now removed and the 
cutter is revolved 
downward through the exact angle required for clearance. This 
angle is read directly from the dial on the headstock of the grinder. 
The spindle must now be locked in position by means of the set- 




Fig. 194 




POSITION BEFORE KAISINS 



Fig. 195 



A Treatise on Milling and Milling Machines 205 



screw D. After this the work is again adjusted vertically until the 
same point of the cutter tooth rests on the tooth gauge as before and 
the cutter is in position for sharpening. The toothrest is now placed 
against the tooth at this same point immediately in front of the 






\ 




H 



Fig. 196 



emery wheel and secured in position. We are now ready to grind, 
after first unlocking the spindle and removing the setting dog F. 

The three positions which the cutter occupies in relation to the 
grinding wheel are shown in Figs. 193, 194, 195. Reading the clear- 
ance angle direct is a new feature in grinding machines, and is one 
of the greatest importance, since it not only makes the setting of 




Fig. 197 



the machine a much quicker operation, but in addition, it makes 
positive the accurate determination of the required angle. The 
importance of grinding to the correct clearance angle can hardly 
be overestimated. 



206 



The Cincinnati Milling Machine Company 



If a cutter is ground with too much clearance, it is certain to be 
unsatisfactory because of its tendency to dig into the work and cause 
chattering. On the other hand, if it does not have enough clearance, 
the heel of the cutter blade will drag and, of course, the cutter can 




Fig. 198 

not cut. The correct relation of either a cup wheel or a disk wheel 
to the cutter is shown in Fig. 196. A is the clearance angle. 
After that angle which has proven best for a given piece of work has 
been determined by experience, a record should be kept and then, 
by means of the above described device, this clearance angle can be 
duplicated exactly, every time the cutter is sharpened. 




Fig. 199 



However, care must be taken to keep the land, that is, the nar- 
row edge of the blade immediately back of the cutting edge, the 
proper width, about ^". Repeated grindings widen this surface, 
as shown in Fig. 197, with the result that although the clearance 




A Treatise on Milling and Milling Machines 207 



angle may be correct, the heel of the blade will drag as indicated at 
A. Such cutters usually give rise to the belief that there is not enough 
clearance and the cutter is reground with a greater clearance angle 
as shown in Fig. 198. When it is again reset on the milling machine 
the heel will not drag but the cutter will have too much clearance 
and be unsatisfactory. 




Fig. 200 

Renewing Worn Cutters. Fig. 199 shows the proper method 
to pursue. The cutter should be placed in the grinder and set at a 
sufficient angle to grind the entire heel of the blade away, pretty 
much as we would do were we to anneal and remill the cutter. In 
this way we can practically renew the cutter by restoring the land 
to the proper width. For this work it is best to use a cup-shaped 
wheel and the cutter can be raised up high enough so that the blade 
next to the one being ground will clear the wheel. After this has 
been done the cutter can be ground to the correct clearance as shown 
in Fig. 196. By this method of renewing cutters their length of 
life can be very much increased. 

A Correctly Sharpened Cutter. An example of correct cutter 
sharpening is shown in Fig. 200. This is one of a gang of side mills 
that were sharpened for milling cast iron. The sketch shows a land 



208 



The Cincinnati Milling Machine Company 



of ^", and this land is ground at an angle of 6°. This is the clear- 
ance angle. Then the tooth of the cutter is ground down immediately 
behind the land at about 12°. This angle should be left as small as 
permissible, its only purpose being to prevent the heel of the cutter 
from dragging on the work. 




Fig. 201. Face Teeth, Shell End Mill 



3 // 
64 



The side teeth are ground in exactly the same way, with a 
land, a 6° cutting clearance, and then backed off 12°. If these cut- 
ters were to be used on steel the proper peripheral clearance would 
be probably 4° instead of 6°, and the same is true of the clearance 
for the side teeth. When cutters like this show a tendency to 
chatter it is best to reduce the clearance on the side teeth. On 




Fig. 202. Blades, Hand Reamer 



some work this may be reduced to as small as 1°, and conditions 
will be improved still farther if the sides are somewhat hollow 
ground; that is, if the face of the cutter is thinner at the inner 



A Treatise on Milling and Milling Machines 209 

end A of the side teeth than at the outer end B. No fixed rules can 
be given for the clearance angles on cutters. This depends on the 
material being milled, the depth of cut, the style of cutter, etc. 
In general practice 5° to 7° for cast iron and 3° to 4° for machinery 
steel will be found quite satisfactory for spiral mills. 

In Fig. 201 the machine is shown sharpening the end teeth of a 
shell end mill. The mill is held on its shank in the spindle of the 




Fig. 203. Periphera Teeth, Large Face Mill 

grinder exactly as it is held in the spindle of a milling machine. It 
can not shift endwise and is freely revolved by turning the spindle. 
The clearance angle which experience has shown to be correct is 
read direct from the graduated dial on the grinder head. 

Hand reamers are sharpened as shown in Fig. 202. For such 
work the face of a cup-shaped wheel is used. The setting for clear- 
ance is the same as for a milling cutter. For all this work the same 
toothrest is used. There is only one universal toothrest necessary 
for the range of work done on this machine. The blade is set in a 
clapper-box which easily yields when the cutter is revolved to bring 
the next tooth in position, and the heavy gauge steel blade forms 
a solid support for the cutter when grinding. 

For the sharpening operations the machine is provided with a 
lever feed. The lever can be adjusted to any position around the 
machine that is handiest for the operator. The swivel head has a 
No. 12 B. & S. taper hole with collets to bush down to the other 
standard tapers used on milling cutters so that all cutters can be 
held on their own shanks as when in place on a milling machine. 

In Fig. 203 the machine is shown sharpening the peripheral 
teeth of a large face mill. The mill is held on a shank which fits into 
the taper hole of the spindle in exactly the same way as the end 



210 



The Cincinnati Milling Machine Company 



mill in Fig. 187 is held, and the same principles as described in the 
preceding paragraphs are followed in setting for the proper clear- 
ance. 

Face mills should have the corners of the blades ground approxi- 
mately round to a y$" radius, as shown in Fig. 204. This is done by 
first grinding to a 45° angle and then again grinding off the corners 
by first setting the machine to 22^° and then to 67^°. The face 
edges of the blades of face mills should have a land about ^" wide 
and the balance of the blade should be ground off at an angle of 
about 7° or 10° towards the center of the cutter. 

Gear Cutter Sharpening. Gear cutters are all made as patent 
relieved cutters and can be ground on the face without changing 
their shape. However, it must be remembered that the shape of 
the tooth is preserved only if the cutter is ground radially. As 
soon as the face of the tooth has been ground away from radial, then 
it will cut a gear tooth of a different 
shape than the original section of the 
gear cutter. In order to have all 
teeth of the cutter do an approxi- 
mately equal amount of work, they 
must all be at the same distance from 
the center of the cutter. To grind 
such cutters properly, we must not 
depend on the correctness of the 
spacing of the cutter teeth, for, 
though this spacing may have been 
indexed accurately when the cutter 
was being milled, it may have 
changed somewhat in hardening. 
In order to grind gear cutters cor- 
rectly we should grind the back of 
each tooth before using the new cut- 
ter. This back should be located from some section of the tooth 
curve and it makes no difference from which section. We should, 
therefore, place a stop somewhere on our grinding device, place the 
top of a tooth against this stop and grind the back of that tooth. 
Then lift the cutter away from the stop, turn it one tooth and locate 
the top of the next tooth against this same stop; then grind the 
back of this tooth, and so on. In this manner we get the backs of 
all the teeth in the same relation to a normal section of the tooth. 




Fig. 204 



A Treatise on Milling and Milling Machines 211 



Now when we want to resharpen the cutter at any time, we simply 
place the back of the tooth against the toothrest while we are 
grinding the cutting face, and all we then need to take care of is to 
grind these faces radially. 

The Correct Way to Sharpen Gear Cutters. In order to 
sharpen gear cutters correctly, it is necessary that the feed of the 
cutter to the grinding wheel should be a rotary or circular feed. 
This is provided for in the Patented Gear Cutter Sharpening Attach- 
ment of the Cincinnati Cutter Grinders. It is shown in operation 
in Fig. 205. The gauge B is swung around to line up with the face 




Fig. 205. The Cincinnati Patented Gear Cutter Sharpening Attachment 

of the tooth and the cutter is set to this gauge. At the same time 
we adjust the spring pawl to the back of the tooth. Then, during 
the grinding process, the cutter is adjusted radially to the grinding 
wheel by means of the adjusting screws A. The effect of this is 
clearly shown in Fig. 206. 

With this device the faces of the teeth will always be ground 
radially, no matter how much is taken off at one grinding. The 
only variation from the radial line will be that due to the wear of the 
grinding wheel, when cutters have been very dull, requiring a great 
deal of grinding. In such extreme cases, after the teeth are ground 
sharp, it is best to reset the cutter to the gauge as in the beginning 
and then grind all of them once more, taking only a light cut. 

The ordinary gear cutter sharpening machine or attachment 
provides for radial setting when putting the cutter in position for 



212 



The Cincinnati Milling Machine Company 



grinding, but on such machines the adjustment of the work to the 
grinding wheel is done by using the cross feed or the table feed, which 
brings the work straight to the wheel. This results in grinding 
along a line parallel with the radial line as shown in Fig. 207, but 
not on the radial line. The more ground off at such a setting, the 



■::/ 



(Drindinq- 
Wheel ° 




Line parallel to. 
radius on which 
toofh is correctly 
ground 



Line parallel to radius 
on nnich tooth is. 
'incorrectly ground 




Line of ad justment of 
work to grinding wheel 



Fig. 206 



Fig. 207 



more the cutter will be spoiled. The original outline is lost and 
perfect gears can not be cut by a cutter deformed by this method 
of sharpening. 

We publish a separate book which shows the Nos. 1 and V/2 
Cincinnati Cutter and Tool Grinders in operation on a variety of 
work, and gives complete instructions for their use. This book is 
sent free on application. 



A Treatise on Milling and Milling Machines 213 



CHAPTER XI 

POWER REQUIRED TO DO MILLING 

When a given piece of work is to be milled we must first decide 
upon the machine on which the work shall be done. In order to reach 
this decision we must know the cutting capacity of the machine. The 
normal horsepower of the machine is usually given in the specifi- 
cations printed in milling machine catalogs. When this is not given 
we can very easily figure the horsepower of a Cone-Driven Machine 
if we know the size of the cone steps and the back gear ratio, and 
that of a High-Power Machine if we know the width and speed 
of the driving pulley. 

The Driving Power of a Milling Machine 

Cone-Driven Machines. Example: To figure the horse- 
power of a Cone-Driven Machine, assuming a No. 3 Plain Cone Type 
Cincinnati Miller that is to run at 74 revolutions. The speed plate 
shows for 74 revolutions — 

Belt on large cone step. 
Second back gear in. 
Countershaft 260 revolutions. 

We have the following data to go by: 
Diameter large cone step = 12". 
Width of belt = 3y 2 ". 
Second back gear ratio = 3.15 to 1. 

The speed of the driving cone is therefore — 
3.15 x 74 (the speed of the spindle) = 233.1 rev. 

Assuming a belt pull of 50 lbs. per inch width of belt, our formula 
now is — 

Diameter of cone step in inches x 3.1416 x speed 

of pulley x 50 lbs. x width of belt TT ^ . .. 
= H. P. delivered 

12 x 33 > 000 to machine. 



214 The Cincinnati Milling Machine Company 

Substituting our values in the above equation, we get — 

12 x 3.1416 x 233.1 x 50 x 3.5 n u 

— = o.y horsepower delivered 

12 x 33,000 tQ the machine . 

It must be remembered that for a Cone-Driven Machine the 
horsepower must be figured separately for each speed. 

High Power Machines. Example: To figure the horse- 
power of a Constant Speed Drive Machine: The horsepower de- 
livered to a No. 2 Plain High Power Machine is found from the 
following data: 

Diameter of pulley = 18''. 
Width of belt = 3". 
Belt pull = 50 lbs. per inch width. 
Speed of pulley = 325 rev. 

Substituting in the above formula, we have — 
18 x 3.1416 x 325 x 50 x 3 



12 x 33,000 



= 7 horsepower. 



The catalog motor rating of this machine is 7J^ horsepower. Since 
the belt runs at constant speed, we can safely assume for present pur- 
poses that the High Power Machine delivers the same horsepower 
at the cutter for all speeds. 

Gutting Capacity of Machine in Cubic Inches. The next 
thing to be determined is the amount of metal the machine equipped 
with the cutter to be used may reasonably be expected to remove 
per horsepower per minute. This will determine the feed that the 
machine can pull on the cut to be taken. We must now turn to 
tables A, B, C, D and E, on pages 178, 179, 180, 181, 182. The cuts 
shown there are maximum cuts and will serve as a safe guide 
if we reduce them by about J^, and are sure to also take into consider- 
ation the depth and width of cut, the style of cutter used and the 
quality of material being milled. 

Example: Assuming a No. 2 Plain High-Power Machine is equip- 
ped with a modern Cincinnati design spiral mill, and that it is to 
take a cut y% deep, 3" wide in machinery steel. Has this machine 
the capacity to take this cut, and if so, at what maximum feed? 
Table B, page 179, shows that for a cut ^" deep, 5" wide, cutter A 
removed 1.074 cubic inches per horsepower a minute. This is some- 



A Treatise on Milling and Milling Machines 215 

what less than the metal removed in the deeper cuts, shown in tables 
C, page 180, and D, page 181. We will assume that for all practical 
purposes % cubic inch is a safe figure for a y cut. 

The No. 2 Plain High-Power Machine has a catalog motor rating 
oilYi horsepower. Seven and one-half horsepower at the machine 
should on the above assumption remove 5^ cubic inches of steel 
per minute. Our cut y% x 3" has a %" section, and the machine 
working within its normal rating will therefore pull this cut at a 
feed of 5^ divided by %, or 15" per minute. 

Therefore, any feed up to 15" per minute may be used. The 
actual feed to be used must be determined by the other conditions 
under which the work must be milled. 

Capacity of Cutters for Milling Cast Iron. It is well known 
that the cutting qualities of different castings vary considerably, 
but as a basis for estimating we will assume castings having the 
tough, close-grained, free-cutting quality of the better grade of 
iron used in machine tools. For such iron, we recommend that the 
figures in tables A, B, C, D and E, after being reduced by about 
one-fourth as above, be multiplied by 1.75 in each case to determine 
the cubic inches of cast iron that can be removed by one horsepower 
in one minute. For harder grades of iron a smaller factor must be 
used. 

Applying this to the above example, we get — 

% cubic inch x 1.75 = 1^ cubic inches. 

A iy<i horsepower machine will therefore remove 9.8 cubic inches 
cast iron per minute. Since the cut has a y% section, it is clear that 
the machine has the capacity to pull this cut at about 25" per 
minute feed. 

Cutting Capacity of Standard Cutters. Tables B, C, D and 
E are based on the use of modern design cutters. When estimating 
on milling work that is to be done with standard high-speed steel 
spiral mills as carried in stock by dealers, it may be best to use the 
results obtained in table A as a basis, taking into consideration the 
number of teeth in the cutter to be used. 

Other Factors Governing Production. All of the above of 
course applies to maximum cuts. When the cut to be taken is known 
to be well within the capacity of the machine, there is no need of 
going through the above calculations, and the feed rate to be used 
must be selected to suit the following factors. 



216 The Cincinnati Milling Machine Company 

a. The strength of the work. 

b. The capacity of the cutter. 

c. The quality of finish wanted. 

d. The accuracy required. 

Since these items depend wholly on the character of each indi- 
vidual case, no data can be formulated for determining their influence 
on the feed rate. 

Other factors entering into production are the handiness of the 
machine, and whether or not it is equipped with a power quick 
traverse and return, the method of milling followed and the extent 
to which jigs and fixtures are used. All of these things are treated 
in separate chapters under these headings. 



A Treatise on Milling and Milling Machines 217 



CHAPTER XII 

VARIOUS METHODS OF MILLING 

In the great majority of shops the milling department is one of 
the most important departments. This is especially so in shops 
that manufacture a large number of duplicate parts. In such a 
shop any reduction of the time required for a milling operation is an 
important item of economy and justifies the management in spend- 
ing some time and effort to determine the best way in which such a 
milling operation might be carried on. This refers not only to shops 
where thousands of similar pieces are made every year, but applies 
equally well to the ordinary manufacturing machine shop where 
lots of 20 or 30 are the rule, and large lots the exception. 

When we have to do a milling operation on a piece of work, we 
know, of course, that we must have a suitable cutter and some device 
to hold the piece. If the number of pieces justifies it we make a spe- 
cial holding fixture, and perhaps a special cutter, and then we are in- 
clined to think that we have done all that can be done. 

However, in a large number of cases a more thorough examination 
will reveal the fact that the operation can be done in various ways, 
and a little study of the elements of the operation will soon show 
which method is the quickest. Take for example, a little bracket of 
cast iron, the foot of which is to be milled flat for bolting it to the 
frame of a machine. One cut will be enough to give the desired finish. 
No particular fixture is required to hold the piece as it can be easily 
held in an All-Steel Vise. No special cutter is required as the operation 
is straight slabbing. It would seem that this operation is so simple 
in all its elements that one method should be as good as another. 
Yet, this operation can be done in several different ways and with 
different degrees of economy. We may use a single vise as the 
average man would probably do; or we might use two vises, one 
behind the other, using the same kind of cutter; or we might design 
a special fixture which will hold a number of these pieces, one behind 
the other; or we might make a fixture which will hold a couple 
of pieces side by side, and perhaps two or three series of these pieces 
in tandem; or we might put the job on a Vertical Miller with one 



218 The Cincinnati Milling Machine Company 

vise, or with two vises, or with a special fixture; or we may build 
a special fixture and mount it on the Circular Milling Attachment. 
Here, then, are a number of methods for doing this simple operation. 
To more easily analyze this let us select a piece of cast iron 2" x 4", 
with straight sides, so that it can easily be held in the vise. Assume 
a cutting speed of 60 feet and a feed of .080 for the desired finish. 
Further, assume y% of material to be removed. With these data 
before us we will analyze some of the methods above mentioned. 

First Method — Using One Vise. Place one vise on the Milling 
Machine table and use a spiral cutter 3" in diameter and long enough 
to cover the 4" width of the piece. As the thickness of stock to be 
removed is }/% , the cutter must travel practically %" before the 
center of the cutter comes to the edge of the work so that the total 
length of the feed will be 2%". A3" cutter running at 60 feet per 
minute runs 76 revolutions per minute, and, as the feed per revolu- 
tion is .080, it will feed practically 6" per minute, so that the time 
required for the cut is ^ of a minute, or practically 26 seconds. 
The machine must now be stopped, the piece removed, the table 
returned and a new piece put in place. Allow for stopping the ma- 
chine 5 seconds, for removing the piece 10 seconds, returning the 
table 5 seconds, inserting a new piece 10 seconds, starting the machine 
3 seconds, altogether 33 seconds. This, added to the 26 seconds for 
milling, makes 59 seconds for the entire operation. It should be 
kept in mind that all figures given here are merely assumed and are 
only used for comparison. 

Second Method — Using Two Vises. Use two vises facing 
each other and placed lengthwise on the table. The operation is as 
follows: Put a piece in first vise; start machine. While milling the 
first piece put a piece in the second vise. When first piece is milled 
throw out feed and advance table so as to bring the second piece to 
cutter. Throw in feed, and while milling second piece remove first 
piece. When second piece is finished stop machine, remove second 
piece, return table and start the cycle over. Keeping the same ele- 
ments as before, we will find the time required for two pieces as 
follows: Inserting first piece 10 seconds, start machine 3 seconds, 
mill first piece 26 seconds, disengage feed 2 seconds, advance table 
8 seconds, engage feed 2 seconds, mill second piece 26 seconds, 
stop machine 5 seconds, remove piece 10 seconds, return table 10 
seconds, altogether 102 seconds, or 51 seconds per piece. Consider- 
ing that we gained 8 seconds per piece, this second method is 



A Treatise on Milling and Milling Machines 219 

better than the first, when we have a large number of pieces to 
mill. 

Third Method — Using a String Jig. Use a special holding 
device in which pieces are placed tandem. Such a device is usually 
called a string jig. Arrange the jig so that the pieces are very close 
together with only about yq" between them. Assuming 10 pieces 
in the jig, we proceed as follows: Put first piece in jig, advance the 
table, start machine, and while milling put in all the other pieces. As 
soon as the last piece is put in the jig, start removing pieces at the other 
end and stop the machine when the last piece has just passed the 
cutter. Time it so that only this last piece has to be removed when the 
machine is standing still. As each piece requires one extra -&', allow 
27 seconds for the milling time instead of 26 seconds. But this is only 
for the first piece. All other pieces are milled in a shorter time, 
because the cutter is still on the first piece when it is entering the 
second. In other words, we do not need to make allowance for the 
Y% " approach on each piece. Altogether the length to be milled is 
10 times 2" plus 9 times tr" plus h /% approach for the first piece. 
Altogether 21 1 V / . This will be accomplished in 210 seconds. We 
must now also consider the fact that the first piece is so short that it 
would be dangerous for the operator to insert the second piece while 
the first is being milled. He will therefore insert two pieces before 
he starts the machine. He will also leave two pieces to be removed 
when he stops the machine. We now find the time for ten pieces 
as follows: Inserting first two pieces 20 seconds, starting machine 
5 seconds, stopping machine 5 seconds, removing two last pieces 
20 seconds, returning table 15 seconds; altogether 65 seconds, 
plus the 210 seconds for milling, or 275 seconds. This is 273^ 
seconds per piece or less than half the time required by the first 
method. 

It might be asked here if it is possible for the operator to 
insert and remove 8 pieces during the milling time. As we allow 
10 seconds for inserting and 10 seconds for removing one piece, it 
will take 160 seconds to insert and remove 8 pieces, whereas the cut- 
ting time is 210 seconds. The operator has therefore a margin of 
50 seconds. The time required to place the jig on the milling 
machine is no greater than that required for one vise. If, therefore, 
the quantity of pieces to be milled per year is large enough to 
justify the expense of the fixture, this method should have the prefer- 
ence over the first and second methods. In considering the gain made 
we should not only consider the saving in labor cost, but also the im- 



220 



The Cincinnati Milling Machine Company 



portant fact that an expensive machine is made available for some 
other operation. 

We will not consider all the possible methods, but only enough 
to indicate how a variation of method may affect the output. 

Fourth Method — Vertical Milling with One Vise. Using a 
Vertical Milling Machine with a ky 2 " diameter end mill and one 
vise, holding the piece as in first method. The approach of this 
cutter is IJ4"; in other words the total feed should not be less than 
3)4". If the nature of the finish of the piece should require it we 
would have to go clear across the piece; in other words the feed 
would be the width of the piece plus the diameter of the cutter, 
which is 6^". We see at once that under these conditions this 
method is slower than any of the previous ones. If the nature of 




Fig. 208 

Showing relation of overtravel of cutter to effective travel. 



the finish is such that we can stop the machine as soon as the entire 
surface has been milled, we get the following conditions: Insert 
piece, advance the table, start machine, mill, stop machine, advance 
table far enough so as to clear mill, remove piece and start new cycle. 
We must not forget that a face mill does not make the ridges or revo- 
lution marks produced by a spiral mill, so that we may use a coarser 
feed, say .120 per revolution. We must further remember that, with 
the same cutting speed the face mill runs only 51 r. p. m. This will 
make the feed per minute 6.12", and the time to pass over a piece 
30 seconds. We find the time as follows: Insert piece 10 seconds, 
start machine 5 seconds, mill across 30 seconds, stop machine 5 



A Treatise on Milling and Milling Machines 221 



seconds, advance table 3 seconds, remove piece 10 seconds; total 
63 seconds, which is slower than on the horizontal machine. 

Fifth Method — Vertical Milling with Two Vises. Use two 

vises on a Vertical Machine. This method will be exactly like the 
previous one, except that we remove one piece and insert the next 
one, while the piece in the other vise is being milled. We find for 




Fig. 209 

No. 2 Vertical with 20" Circular Attachment, milling gray iron castings V/% x 4^* 
at the rate of 220 per hour. 

the complete cycle covering the two pieces the following, keeping 
in mind that the machine never needs to be stopped: Insert first 
piece 10 seconds, advance table to cutter 5 seconds, engage feed 1 
second, mill 30 seconds; while milling, remove 
and insert piece in other vise; disengage feed 
1 second, advance table 5 seconds, engage feed 
1 second, mill second piece 30 seconds, disen- 
gage feed 1 second, advance table 3 seconds 
and start new cycle. Total time for two pieces 
87 seconds, or time per piece 43 3^ seconds. 

The Relation of Face Milling to Using 
a Cutter on an Arbor. It will be noted that 




473 L 



Fi*. 210 



222 



The Cincinnati Milling Machine Company 



we always put the piece in the vise or fixture with its broad side 
toward the cutter. This seems quite natural because the feed will 
then be along the short side; in other words, we will have to feed 
2" instead of 4". There is absolutely no doubt about it that this 
is the quickest way when we use the horizontal machine and a 
spiral cutter, but when we use the vertical machine and an end 
mill, conditions have been changed and it may be well to analyze 




Fig. 211 

No. 2 Vertical Miller with 20" circular attachment and special fixture milling 
sad irons 4" x 6J^", ready for polishing, at the rate of 2 per minute. 

this somewhat closer. Offering the broad side to the cutter requires 
a M/i' cutter; offering the narrow side to the cutter requires only a 
23^" cutter. The Ay/ cutter requires an approach of 1M"« Plac- 
ing the piece with the narrow side to the cutter requires an approach 



of only Y/. The 2y cutter can run 
4 1 /^" cutter or 102 revolutions. Using 
the same feed of .120" per revolution we 
get 12.24" feed per minute. The length 
of cut on each piece is the approach of 
y 2 " plus the length of 4" or 4^". The 
time for the cut will, therefore, be 22 
seconds. All the other factors remain 
the same. The time for two pieces is, 
therefore, 71 seconds or 35J^ seconds per 



7 a times as fast as the 




Fig. 212 






A Treatise on Milling and Milling Machines 223 



piece, showing that it is actually more economical to mill the long 
way across this piece when using a Vertical Machine. This is better 
than the time required when using two vises on the horizontal 
machine. However, the gain due to the faster feed has been offset 
to a great extent by the greater travel required because of the 
diameter of the cutter. 

Influence of Diameter of Face or End Mill. Figure 208 
shows the relation of the 4J/£* diameter cutter to the work and also 
how the "approach" distance must be figured when estimating on 
face milling. When the cutter first touches the work its center is at 
A. When it has moved to B it will have covered the full width of 
the piece. In other words, it is necessary to travel from A to B to 
bring the cutter fully into the work. This is 134"- In order to 
traverse the work completely the cutter must move from B to C, 
which is the same as the width of the piece, 2". The total travel 
therefore, is the width of the piece plus the "approach," or 3J4"- 
The quality of finish required makes it advisable in many cases to 

continue the travel until 
the cutter has entirely 
cleared the work. If we 
wish to do this then the 
additional travel will be 
the width of the piece 
plus the distance DE, or 
2" plus 1J£», or 3Ji", 
making the total travel 
for milling the piece 63/£". 
Because of the long "ap- 
proach" and the long 
overtravel required on 
most work, face milling 
on a single piece like this 
is not economical even 
though it does permit of 
faster feeds. 




Fig. 213 

Locating work in fixture for circular or continuous milling. 



Continuous Vertical 
Milling. Still another 
method which might be employed for this piece would be to place a 
special fixture on a Circular Attachment somewhat like the illus- 
trations, Fig. 209 or Fig. 211. With such an arrangement the 



224 



The Cincinnati Milling Machine Company 



operator stands at the loading position and does nothing but take 
finished pieces out and put new pieces in, while the cutter mills some 
other piece. With such an arrangement there is no time lost. There 
are three possibilities: First, the operator removes and chucks a 
piece in the time in which a piece is completely milled, and both 




Fig. 214 

Continuous milling with hand operated fixture illustrating advantage of contin- 
uous milling when chucking time ie longer than milling time. Done on No. 3 High- 
Power Miller with 20" Circular Attachment. Surfaces \%" x 4%", cut M" deep; pro- 
duction V/i pieces per minute. 

machine and operator are working to the maximum of their capacity. 

This represents the highest possible economy. The second possibility 

is that the milling takes longer than the chucking. In that case 

the machine works to its full capacity and the operator does as 

much useful work as he can. A third possibility 

is that the milling is done so rapidly that it is not 

possible for the operator to remove and insert a 

piece in the short time required to mill one. In 

that case it is necessary to slow down the feed 

until the milling is done slow enough to allow the 

operator to remove and chuck a piece while another 

piece is being milled. Even with this apparently perfect device there 




Fig. 215 

Material, Steel. 



A Treatise on Milling and Milling Machines 225 

is room for further study. There are various things which affect 
the time required to complete a piece, such as, for instance, the 
size of the cutter, the diameter of the holding fixture, the distance 
between the pieces in the holding fixture and even the way in which 
we place the pieces, whether lengthwise or crosswise. The space 
of this book forbids us to go into all these points in detail, but we 
will illustrate how the placing of the piece and the diameter of the 
fixture become elements of final economy. 

Let us assume again that we want to mill a little bracket, 4" x 2", 
and that we employ a fixture bolted to the Circular Milling Attach- 
ment as shown in diagram, Fig. 213. The outside diameter of this 
device is 30" and the piece is to be placed as shown at A and B. For 
the purpose of chucking we will allow %" between the inner edges 
of the two adjacent pieces. In that case there is a distance of 3^" 
between the points A and B, so that the cutter has to travel 3%" 
in order to finish one piece complete. Assuming a 4J^" cutter and 
the same feeds and speeds as in the previous examples, we find that 
it takes 37 seconds to mill one piece. If we had placed them as 
shown at C and D of the diagram, again allowing y± between two 
adjacent pieces for the purpose of chucking, we would find that there 
is a distance of 53^" between the points C and D, and as we now 
use a 23^2" cutter, we would do the milling complete in 30 seconds. 
This shows how the placing of the piece in the fixture influences the 
time required. If we had chosen a fixture 18" in diameter, then the 
distance between the points C and D would have been 6 1 / 9 " and the 
time per piece would have been 34 seconds. This shows how the 
diameter of the fixture influences the time, at least to a certain 
extent. 

In many cases the time of chucking is considerably more than the 
time of milling. In all such cases an attempt should be made to do 
the milling continuously, because then all the time of milling is 
saved, and the time of the entire operation becomes merely the time 
required by the operator to do the chucking. In such a case it makes 
absolutely no difference how we do the milling, whether with a 
larger or smaller cutter, because we have to make the milling time 
sufficiently long to permit the operator to chuck a piece. Fig. 214 
shows a case of this nature. Steel pole pieces for a self-starter are 
being milled. It will be noted that the surfaces to be milled have 
considerable idle space between them, but this is of no importance, 
as it takes the operator longer to chuck than it takes the cutter 



226 



The Cincinnati Milling Machine Company 



to mill. It should be noted that in this case a pair of interlocking 
helical mills is used. 

Automatic Clamping and Releasing Fixture. Sometimes 
it is practical to make a simple automatic clamping device part of 
the fixture, in which case the operator would do nothing except 




Fig. 216 

Continuous milling with an automatic clamping and releasing fixture. Pieces 
are produced at the rate of 20 per minute. 

remove a milled piece and put a new piece in place, leaving the clamp- 
ing to the fixture itself. Fig. 216 shows such a device. As the 
attachment rotates a hardened 
steel plate passing under a roller 
bears on the clamping device and 
holds the piece securely while it 
passes under the cutter. Shortly 
after it has passed the cutter the 
clamping is released, permitting 
the operator to remove the piece 
when it arrives at the loading posi- MatSSi, 2 Braas. 




A Treatise on Milling and Milling Machines 227 

tion. Under those conditions it takes more time to mill than to 
handle a piece and the total time becomes exceedingly short. The 
pieces shown in the illustration are regularly milled at the rate of 
20 per minute. It will be seen that in this case the distance between 
two adjoining pieces is as short as it can be made and yet take 
care of the unavoidable variations in the size of the pieces. In 
other words, the cutter does not have to travel over idle spaces, 
and all the time consumed is actual cutting time. 

The Index Base Method. This method of continuous mill- 
ing was devised in connection with Cincinnati Automatic Millers. 
The index base as described on page 59 is made in two sizes to suit 
the 24" and 48" Automatics. 

Fixtures are mounted at each end of the swiveling table as in 
Fig. 218. While the pieces in one set of fixtures are being milled 
the operator chucks pieces in the other set of fixtures. The machine 
automatically reverses and returns, while the operator indexes the 
fixture 180° to bring the newly chucked pieces in position for milling. 

This makes the process continuous. The operator need not 
leave his position and the chucking is always done at the end of the 
table farthest removed from the cutters, thereby insuring a very 
desirable degree of safety. 




Fig. 218 

The 48" Duplex milling two rows of motor frames, 43^" 
wide, at 5 5 /% feed. The fixtures are mounted on the 16" 
x 36" Index Base, and the intermittent feed is used. Pro- 
duction, 120 pieces per hour. 

It will be seen from the above that there is room for study as to 
the best method to be employed. One of the main points to be con- 
sidered is the quantity of pieces to be handled, per year and also 



228 The Cincinnati Milling Machine Company 

the quantity made in one lot. If one operation keeps a machine 
constantly employed for months at a time it does not matter if it 
takes a few hours longer to set up the machine and fixture, but if 
the pieces come through in relatively small lots, requiring, say, only 
a day to mill, then it becomes necessary to select some method 
which requires only a short time to set up the machine. What 
would become a negligible time for several months ' ~ork, might 
become prohibitive for a day's work. 



A Treatise on Milling and Milling Machines 229 



CHAPTER XIII 
MILLING JIGS AND FIXTURES* 

The term "milling fixtures" may be understood to cover all de- 
vices used to hold work on the milling machine table in the proper 
position for milling operations. The term, however, does not, as 
generally understood, include the standard bolts, nuts, clamps, 
raising blocks, jacks, etc., that usually form part of the equipment 
of a milling department and are utilized indiscriminately for a 
variety of odd jobs. 

Since the methods of milling are widely varied, it follows that 
there must be an equal variation in the construction of the fixtures, 
this being made still more apparent by the wide divergence in the 
size and character of the work that is handled by each one of the 
standard milling methods. It is consequently impossible in a chapter 
like this to do more than indicate the principles of fixture design and 
to give a few illustrations of typical examples. Before passing on 
to this, however, it will be proper to consider the subject of the 
fixture in conjunction with the method. 

Classification According to Method: Rotary, square or 
reciprocating. In a previous chapter (Various Methods of Milling) 
we have discussed the selection of the method, this being done, 
however, solely with reference to the shape of the piece and the 
degree of accuracy and quality of finish required. No attempt was 
made to show the influence of quantity in this selection. Where 
large quantities of parts have to be machined it becomes less essen- 
tial to take into account the questions of initial cost and maintenance 
cost of the fixture, but where a limited quantity of pieces are 
machined it will often be found necessary to decide between that 
method which would give the highest production, and that method 
which would give the highest production per unit of cost. For 
instance, the tool designer or time setter may be concerned with a 
piece which lends itself very conveniently to the rotary method; 
the piece could also be handled by the right angled or square method, 
and again by the reciprocating method. The production is greatest 

*Most of the fixtures described in this chapter were designed by our Service 
Department for maximum production under the conditions prevailing in the 
customer's shop. 



230 The Cincinnati Milling Machine Company 

with the first named method and least with the last method. How- 
ever, if there are not more than 100 pieces to be made in each 
lot and not more than 12 lots to be handled per year, the question 
of cost of equipment becomes important. Now, if we will assume 
that the rotary method produces the piece in one-third of a minute, 
the total time for the 100 lot will, of course, be 33.3 minutes. The 
square method produces the piece in one-half minute, giving a time 
of 50 minutes, and the reciprocating method in two-thirds of a 
minute, giving a time of 66.6 minutes per lot. Obviously, if we 
were considering continuous production, or even production of such 
quantities as would permit the machine to run for a week without 
changing the job, there could be no further thought given to the 
question of cost of initial equipment, or for that matter to the 
question of cost of upkeep. But under the conditions we have laid 
down we must in addition to the items above specified, consider the 
time taken in setting up. Here again we will use arbitrary figures. 
Setting up the rotary attachment, including the mounting of the 
circular table on the machine, connecting the rotary feed mechanism 
and mounting the fixture on the rotary attachment would consume 
40 minutes;* for the square method of milling, which merely needs 
the setting of the fixture on the table, 20 minutes; and for the 
reciprocating method, 20 minutes also; so that it is apparent at 
once that there is no gain in the total time of the rotary method 
with its higher individual productivity as compared with the square 
method. Therefore, since the square method is the simpler of the 
two, from the standpoint of fixture design and cost, it would take 
precedence. 

Comparing the square method with the reciprocating method 
we have a total time of 70 minutes as against the total time of 
86.6 minutes. This repeated twelve times during the year would 
give us a balance in favor of the square method of 219 minutes, or 
approximately 3J^ hours. We are, therefore, really only justified 
in spending 3 3/2 hours more on the construction of the square fixture 
over and above that we would spend on the construction of the 
reciprocating fixture. All this again on the assumption that it is 
desired to make the fixtures pay for themselves in the course of a 
year. If a different standard is adopted, then this 3^ hours may 
increase to 7, 103^, or even 14 hours. 

*The term "setting up" as above used is also understood to include the 
time taken for tearing down this apparatus and restoring the machine to its 
normal condition. 



A Treatise on Milling and Milling Machines 231 

Skill of Workmen as a Factor. The above comparison deals 
only with the influence of the cost of the fixture on the selection of 
the method. In addition to this there is, of course, to be considered 
the question of how the skill of the available workmen affects the 
degree of complexity permissible in the fixture. 

It is obvious that the simplest arrangement from the operator's 
point of view is the rotary method in which his functions are con- 
fined to those of releasing and removing finished work and inserting 
and clamping the unfinished work, so that here decision would tend 
towards the rotary method. 

The next simplest method would be the reciprocating method, in 
which the table merely travels from left to right and from right to 
left. Here, in addition to his work-handling functions, he must exer- 
cise that of reversing the direction of the table feed and possibly 
moving the table a certain distance either through the hand or 
power quick return. 

The square method calls for most in the way of the operator's 
activity, since he must continue to change the feeds so as to en- 
gage alternately the cross and longitudinal feed and must also re- 
member to reverse such feeds every half cycle. 

Maintenance Cost. Another item to be considered is the cost 
of maintenance or percentage of productive hours of the fixture. 
This must always be in favor of the simplest fixture no matter how 
carefully the design of the others be worked out. The above com- 
parisons have been limited to three methods. No attention has been 
paid to the simple method of holding one piece in a simple vise-like 
fixture which would, in all probability, be the most suitable method 
to employ for a job that is run through in the quantities we have 
selected. It is largely because this method would be so obviously 
the correct one that we have omitted it from the comparisons, 
the only purpose of which is to indicate the different points to be 
watched in arriving at a correct decision as to the selection of 
methods. 

Summarizing the above, therefore, and leaving the question of the 
simple fixture out of consideration, it appears that from the point 
of view of production the decision lies between the rotary and square 
methods. From the point of view of cost of fixture the decision 
favors the reciprocating method. The quality of help again favors 
the rotary method and the maintenance cost the reciprocating 
method. It is reasonably obvious that the simplest or reciprocating 
method wins most points in this contest and the fixture will probably 
be made along these lines. 



232 The Cincinnati Milling Machine Company 

It is, of course, understood that all of the foregoing analyses 
should properly be made by the time study department in con- 
junction with the fixture designing department. 

Much of the matter discussed does not properly pertain 
to a discussion of fixtures. It has been found desirable, however, 
to insert it at this point, since there is really no exact point of sever- 
ance between the tool designing and time setting departments. It 
will further be understood that immediately the quantities that have 
been used in the above illustration shall change, they being made 
larger or smaller, a completely changed set of figures have to be con- 
sidered which will probably lead to entirely different conclusions. 

Apart from the classifications of fixtures according to methods, 
there is an additional classification that can be made between those 
fixtures which must locate the work with reference to a cast surface, 
either plain, bosses or cores, and those which must locate the work 
from some surface or surfaces previously machined, these surfaces 
again being either plain, circular or formed. Still another classi- 
fication may be made between those fixtures which are concerned 
only with the production of one surface at an operation and so call 
for no relative motion between the work and the table and those 
which must produce two or more separate surfaces, or else a con- 
tinuation of the first surface either with gaps or projections between. 
There is still another classification which is that of fixtures in which 
the feeding mechanism is contained in the fixture, the milling 
machine table itself merely being regarded as a means for the 
preliminary adjustments between cutter and work. 

In addition to these classifications there must be considered the 
question of the capacity of the machine. It may very well happen 
that the limitations of power in the machine are such as to render 
the chucking time a very negligible portion of the total time con- 
sumed, so that if the operation is scheduled for such a low-power 
miller, a different method of chucking the work will be used than 
that which would be proper if a powerful machine with adequate 
feeding facilities were employed. Of course, under ideal conditions, 
the power of the machine should always be sufficient to feed the 
work past the cutter at a rate governed only by the ability of the 
work to withstand the feed pressure, or by the degree of finish that is 
required. The next governing factor may be the ability of the 
cutter to withstand these strains, but outside of these factors there 
ought to be no limitation imposed on productive milling through 
any weakness of the machine. 




A Treatise on Milling and Milling Machines 233 



Axioms for the Fixture Designer. There are, however, in all 
these classifications certain well-defined principles, most of which 
are concerned with adequately clamping and supporting the work. 
Stating these in the form of axioms, since they are mostly self- 
evident, we have: 

First. The clamp should be immediately above the support- 
ing point. 

Note — Disregard of this leads to springing of the work, or lifting of the 
work due to support point being transformed into a fulcrum. 

Second. Three fixed supporting points should be the maximum 
for any rough surfaces. 

Third. Supporting points for finished surfaces should be as 
small in area as is consistent with the pressure to be exerted by the 
clamps. 

Fourth. All supporting points should be set as far apart as 
the nature of the work will allow. 

Fifth. All side clamps should be arranged to press downward. 

Sixth. The fixed supporting points should always circum- 
scribe the center of gravity of the work. 

Seventh. All supporting points over and above the original 
three should be sensitive in their adjustment. 

Eighth. All clamps and adjusting supports should be operated 
from the front of the fixture. 

Ninth. All clamps and support points that are operated or 
locked by wrench should have the same size head. 

Tenth. Support points should be set so high above the body 
of the fixture as to minimize the amount of cleaning required. 

Eleventh. Support points should have provision for easy 
removing and replacing in the event of breakage. 

Twelfth. Fixed support points should have provision for 
adjustments to take care of variations in castings from time to 
time. 

Thirteenth. Clamps should be arranged so that they can be 
easily withdrawn from the work. 

Note — This is to avoid lengthy unscrewing of the nut in order to give 
ample clearance between clamp and work. 

Fourteenth. Springs should be used to hold clamp up against 

clamping nut. 

Note — This is to avoid the falling down of the clamp and the consequent 
loss of time attendant on holding it up while inserting the work beneath. 



■ : i 



The Cincinnati Milling Machine Com? 



rUTH:-::-: - ... ; ..-.-- :- .-. ooo - o: be OJie^ible o: 

::t iTeneoThs honi sni eye 

-o;orij— y. Aieyoaoe ir:"ls;:L :•:: raldnz o; eni hornso so 
:ha: hois —. 17 o:: be ieoenien: o;:o :'ri:Th:n be™ eeo ~ oho oo 1 
oaroo 

All of the above axioms are applicable to almost ever: 
of fixture. 

Ai eo tI-:::^ ::' Eoooe :: 7oe oziioos Fir _11 is :: in:e:eso. This 
does not show a fixture, hot does show a bmtt-up construction of 
damps, supports and blocks for an experimental cut. It will be 
noted that the projecting arms AA of the work have a sofid sup- 
port B between the lower arm and the table; also C between the 
:.::/:.-: >ni 7.— e: ottos :heo hoe 7otots 7 ore se: 5-: hoor :otO~ 
pressure k directly over the supports and that the distance from the 
haroTTor boh o: :he roliroro is from :hnee :: 7. or :iroes :he iisooooie 
7:ro :he bch :: :he p«:±T :: :".in:iig 1: is. ::' eoorse. ;oso is 
iroTorTan": :•: hoserre These o:oonole- in oeoooooory se:-oos es i: ii 
in the design of the finished fixture. 

The other desiderata for good fixture design may be summarized 

os 77 :~ s: 

F irs : : R pic: :y : C i 3. m ; in ^ The majority of fixtures 
erooliy 7: o77inr ne-::r : -n soaoioro honors seroreh ~7h 
sore^s irnoos 7: laihlioaTe The iroserriio in: oeroiThor ibohe^rorh 
:ir honors oroy be ;:.:-"7e. ~ 7o s si:: =.: :hej :an be easily slid 
baole en: ::.:;:_ 7oe hole in hoe 7oror oooy be larre eroorh o: : 

washer used in conjunction enables 
remiTeh es ~::o is hoe too has beer 

. :ases Tarr7oiooh here o rryeioinr 

-In ring :: 7ne honor 0:000: 7oe 7onor- 
provides sufficient clearance. This 
» controlled by a pin set in the clamp- 
nilleh oroond :he hie : too: go oo:. 
7oeo Toe yoaoonTies ;hLSTh'y 7oe aided 
o:s ~o::o :on. :: looorse. 



~7r oonboeo: oo: 
tion with a very firm 
rate several clamping 
- ~ell be used. This 
nultaneous damping 
possibilities of lifting 



A Treatise on Milling and Milling Machines 235 

the work from its supports due to undue pressure being exerted at 
any one point. It can also be so regulated as to give a certain 
desired pressure sufficient to hold the work and need not be sufficient 
to create any distortion. 




Fig. 219 

High-Power Miller with improvised holding devices finishing cast steel passenger car axle 
housing. Cutters 6" and 4* diameter, 32 revolutions, feed i%" per minute. 

Second: Accessibility for Inserting and Removing Work. 

This point must, of course, be watched in all fixture design, but it is 
particularly important where the production is governed solely by 
the chucking time, as in practically all rotary and most reciprocating 
jobs, or when the operation consists of the rapid milling of a small 
surface in a comparatively large and hard-to-handle casting. It is 
not easy to give any particular indications as to how this end is to 
be achieved since the conditions will vary with almost every piece. 

Third: Generous Ducts for the Escape of Chips and 
Lubricant. There are two functions served by the proper obser- 
vance of this rule; first, the lessening of the time required to clean 
the fixture after the work has been removed, which, of course, 
directly influences production; and secondly, the elimination of 



236 The Cincinnati Milling Machine Company 



the danger attendant upon chips remaining on the locating surfaces 
on which the work rests, which, of course, would throw the work 
out of its proper chucking position, and where the location is from a 
previously finished surface would result in spoiled work. 

Fourth: Removal of the Clamping and Supporting Mem- 
bers from the Cutter Zone. The great thing to be considered in 
this is, of course, the safety of the operator. One of the great reasons 
why the Automatic type of machine has met with so much success 
is, that due to the automatic quick return from, and traverse to the 
cutter, the work can be handled at a very safe distance from the 
cutting teeth. This principle should be observed in all jig design, 
whether used on Automatic or Knee and Column machines, and, if 
necessary, extension handles should be provided so that the opera- 
tor's hand never approaches near the cutter. When a string fixture 
is used it is often desirable to have a space between the first and 
second pieces considerably greater than is required for the actual 
dimensions of the job, in order that the act of chucking the second 
piece can be accomplished with greater safety. Here again the exact 
proportions must be worked out, having in mind the length of time 
required for the chucking and cutting operations, the ideal con- 
ditions being reached when the operator's maximum chucking and 
removing effort consumes a time equal to that required to take the 
cut over the complete number of pieces in the fixture. 

Another item to be considered in this connection is the lessened 
danger of the cutter striking the hardened clamps or nuts, which 
results either in breaking or dulling the teeth. 

Fifth: Elimination of Clamping Strains from Table of 
Machine and Absorption of Same in Fixture. While there are 
certain cases where it is not always proper to follow out this rule, 
yet it is in a great majority of cases very applicable. Milling Machine 
tables, by virtue of their necessarily shallow section, are not well 
fitted to withstand the buckling strains that can be set up by clamp- 
ing. It must be remembered that even the heavy table of a planer 
can be buckled by clamping work to it. Such strains being constantly 
transmitted will ultimately result in the distortion of either the 
T-slots or true plane of the table, both of which conditions immedi- 
ately affect the accuracy of the work produced. The fixture should, 
therefore, be designed with sufficient depth to withstand and absorb 
all the clamping strains. This frequently, and in fact, generally, 
means that the base of the fixture should be of a box section. Those 



A Treatise on Milling and Milling Machines 237 

fixtures which consist of a single flat plate with a number of pro- 
jecting bosses can not be regarded as representing the best practice. 
There are, of course, exceptions such as, where the bosses which 
project a good deal above the base of the fixture, provide in them- 
selves a supporting place for the heel of the clamp, for the clamping 
screw and for the supporting screw on which the piece rests. 

Sixth: Provision of Mass in Excess of Necessary Rigidity 
to Absorb Chatter. As has been mentioned in an earlier chapter, 
the milling cutter is the factor which inherently sets up chatter 




Fig. 220 

High-Power Miller with two All-Steel Vises used as tandem fixtures: Gripping rough castings 
for a cut 7" wide, ys" deep with cutters 6" diameter, 42 revolutions, 12.6" feed. Milling time, roughing 
and finishing, including two chuckings, 6 minutes per piece. 

conditions due to the fact that the chip, which theoretically starts 
with a zero thickness, ends up with a maximum according to the 
amount of traverse of the table during the passage of the tooth 
through the work. Since there is no possibility of the cutter biting 
into the work at the commencement of such a stroke, there must be 
a wedging-apart action between tooth and work, which has been 
found to be one of the main causes of chatter. It is, perhaps, proper 
to say that chatter exists in almost every milling job. Where the 



238 The Cincinnati Milling Machine Company 

fixture is just strong enough to withstand the feed pressures and 
cutter pressures, the chatter is likely to be accentuated. If the fixture 
be from four to five times as heavy as is really necessary, much of 
this chatter will be absorbed. There is no reason other than that 
connected with the cost of the cast iron in the fixture, why a milling 




Fig. 221 

No. 2 Plain Cone-Driven Miller cutting recesses %" deep, jfe* wide on both sides of two .60 carbon 
steel bars. Two vises in tandem, each hold two bars, 11^" long, y% thick. Cutters 3H" diameter, 50 
revolutions, .068" (3.4" per minute) feed. Time per piece 2.2 minutes. 

fixture may not be very heavy, since there is but seldom any vertical 
adjusting or handling of the fixture which throws a muscular strain 
on the operator. The difference between drilling jigs and milling 
fixtures in this respect is very marked and the tool designer must 
approach the design of a milling fixture with an entirely different 
conception of proportions than he would use in connection with a 
drill jig. It is impossible to over-emphasize the need for extra 
weight in all milling fixture bodies. 

Now, if we keep all the above factors in mind, we can then con- 
sider the different types of fixture in more detail. 

Vises Used as Fixtures. Wherever possible we should, of 
course, use standard equipment. To this end it very frequently 
happens that one or a pair of standard vises can be utilized to good 
advantage. Fig. 220 shows the use of two Cincinnati All-Steel Vises 
which, with the addition of supporting blocks laid on each side, 



A Treatise on Milling and Milling Machines 239 

form a highly efficient pair of fixtures for this particular operation. 
It will be noted that these vises having a swiveling, movable jaw, 
adapt themselves easily to the irregularities of the casting, and 
further, that the jaw plates being angled at the back, tend to pull 
the work down firmly on the fixed supporting points, which it 
will be noted are as close to the clamping points as is possible. The 
additional adjustable supporting point is brought out to the extreme 




Fig. 222 

No. 2 Plain Cone-Driven Miller cutting slots 1" wide, 9" long, into .60 carbon steel bars, y% thick at 
one cut with helical end mill, 160 revolutions, feed .015" (2.4" per minute) roughing, .068 (10.8") finishing. 
Time for two cuts, two chuckings, per piece, complete, 73^ minutes. 

end of the piece. In the manufacture of rifles, typewriters, adding 
machines and similar parts, very great use is made of a standard 
vise fixture, this fixture being provided with false removable jaws 
which are made to suit the contour of the piece to be held. Such 
vises are usually provided with a cam movement for rapidly opening 
and closing the vise jaws, which movement also gives the maximum 
of gripping effect at the conclusion of the stroke. 

An example of the use of the machine vise is found in Fig. 221, 
which illustrates the use of two plain cast-iron vises with plain jaws, 
holding in each vise two tamp racks. In this case a spacing block 
A is used. It is loosely attached to the vise to prevent its being 
mislaid, or tend to work over into the position occupied 
by the work. This arrangement is, of course, applicable only to 
work that comes within reasonably fine limits of parallelism and 
thickness. The use of two vises permits of the removal of the work 



240 



The Cincinnati Milling Machine Company 



from the one vise while cutting takes place on the other and in con- 
junction with an elevating movement of the knee, also allows of 
the insertion of unfinished work in the same vise, thereby giving a 
continuous milling operation. Fig. 222 shows the same two vises, 
each of which grips one end of the same plate in which it is desired 
to mill a slot. There is nothing that could be devised for this par- 
ticular job that would be more efficient and at the same time less 
costly. 

The foregoing shows finished work held in accurate plain vises. 
The Cincinnati All Steel Vise, page 62, is a very satisfactory fix- 
ture for holding rough forgings and castings. 

An example of this is given in Fig. 223, showing the No. 5 Plain 
High Power Miller milling the top of a Locomotive Eccentric Bar. 
which is held in two All Steel Vises. 

Another use of these vises is shown in Fig. 224. Here two vises 
are used in tandem on the No. 4 Vertical Miller for milling loco- 
motive trailer spring saddle guides. The operator loads one vise 
while the piece in the other is being milled. 





Fig. 223 



Fig. 223-A 

Operation — Mill Top and End- 
Machine — No. 5 Plain High Power. 
Material — Forged Steel. Stock Re- 
moTed— y % ' . Cntter— 3Ji* Dia. Heli- 
cal Mill. Feed — 7J£" per minute. 
Speed — 65 r. p. m. Tune per piece., 
nulled complete — 98 minutes. 



Standard Parts of Fixtures. While on the subject of a standard 
fixture, it is proper to look at what may be regarded as standard 
constructions. There are but few of these, since conditions vary 
so largely in milling fixture design and it has seldom been found 
practical to carry in stock a number of such standard parts as may 
very well be done in connection with the designing of drill jigs. 
However, the use of certain well-defined types even though differing 
in dimensions can be advantageously followed and we will discuss 
a few of these types. 



A Treatise on Milling and Milling Machines 241 




Fig. 224-A 




Fig. 224 
Machine — No. 4 Vertical Miller. Material — Cast 
Steel. Stock Removed— K". Cutter— 4" Dia. Shell End 
Mill. Speed — 41 r. p. m. Feed — V>/% per minute. Time 
per Piece — 28 minutes. 

Support Pins. These are of two types — Fixed and Adjustable. 
The Fixed Support Pins when used in conjunction with a finished 
surface may generally be as Fig. 225, consisting of a flat-headed 
shoulder screw, having a hardened head, the top of which head may 
be surface-ground when in position. No adjustment need be pro- 
vided. When used for supporting rough castings, a good con- 
struction is that shown in Fig. 226, consisting of a screw with hexa- 
gon head and rounded top, tapped into the body of the fixture and 
provided with a lock nut so that the points may be elevated or 
lowered according to the variation in the castings. 

Adjustable Support Points may be divided into two classifica- 
tions: those that are brought into contact with the work through 
a spring and those which are hand-actuated. The first of these is 
shown in Fig. 227 and consists of a plunger which rests on a com- 
pression spring. Its vertical movement is limited by the point of 
a screw which projects over into a slot cut in the plunger. This 
prevents the spring from pushing the plunger far out of the fixture 



242 



The Cincinnati Milling Machine Company 



and is also a preventive against the plunger being lost when the 
fixture is in, or being transported to the toolroom. The plunger is 
clamped in position by either a sleeve directly operated on by a 
screw, or by a split sleeve, both halves of which are pulled together 
with a screw, the first of these methods being shown in the illus- 
tration. It will be evident that in both methods of clamping the 
support is entirely dependent 
upon the friction between the side 
of the plunger and the clamping 
member. For heavy work or work 
where a jarring effect is produced, 
it is desirable to have a more 





Fig. 225 



Fig. 226 



solid form of adjustable support. A standard construction for this 
is shown in Fig. 228, and consists of a vertical plunger guided and 
restricted in its movement by the point of a screw and having its 
lower end beveled at an angle of 45°. This end rests on a similar 
surface on the end of a horizontal sliding plunger which is moved 
forward by a screw in the fixture. This construction has the merit of 
being cheap, simple and self-locking. It is not usually considered 
desirable to put a spring on this plunger to force it down when the 
adjusting screw is released. It is rather better to rely upon the 
operator forcing the plunger down with his finger, which operation 
insures the cleanliness of the top of the supporting point. 

Clamps. The standard constructions of these can again be 
divided into two types: those which press the work directly down 
on to the supporting member and those which hold by a side pres- 
sure, as in the case of vise jaws. The general principles of clamps 
have been touched on, on page 234, and the illustrations here given 



A Treatise on Milling and Milling Machines 243 




Fig. 227 




Fig. 228 




l r-f-r 

I I i 

i * I 

.J..LX. 



Fig. 229 



244 



The Cincinnati Milling Machine Company 



clearly show the application of some of these principles. The 
simplest form of Slotted Clamp, Fig. 229, is provided with a round 
heel and beveled gripping portion. The rounding of the heel is so 
that the clamp may adjust itself on a three-point bearing, two of 
these points being on the work, the third on the supporting part 
of the fixture. Theoretically, such a clamp should be used in con- 
junction with a ball washer, but practically the ordinary flat washer 
serves. 

The Swiveling Clamp, Fig. 230, having the same gripping portion 
and heel is restricted in its swinging by the pin shown in the clamping 
stud. 

The Swinging Clamp, Fig. 231, is used only when the work is 
so large and unwieldy as to require a good deal more space for 
insertion than is usually necessary. This construction consists of 
a clamp swinging around a horizontal axis having provision at the 
gripping end for a one-point contact only, and since its plane of 
swinging is fixed, the clamping bolt swings into the clamp from 
the side so that when the clamp is released the bolt falls down below 
the work and the clamp is swung back entirely behind the pivot. 

The Cam, Fig. 232, has an angled surface, and in the one move- 
ment effects three pressures; it tends to force the work down on 
to the support over against the side stop and up against the end 
stop. 

Clamps which hold by gripping the work sidewise are shown in 
Figs. 233 and 234. The heel of the clamp is angled so that the grip- 
ping of the piece tends also to pull it 
C, —.— down on to the supporting points. It 

vy/ YV\ is usually desirable to serrate or file- 

I ~ " — —— \ 1 cu t the gripping surfaces andthe hole 

must, of course, be slotted in order 
to allow of slight vertical adjust- 
ment. The heel is again rounded 
and a compression spring provided 
to keep the heel of the clamp up 
against the undercut surface of the 
fixture. 

The simplest and one of the most satisfactory standard forms 
of Side Clamp is shown in Fig. 234 and consists of a simple screw 
having a hardened, pointed end, said screw being set to point down- 
ward to an angle of approximately 5°, so that its advance also 
produces a downward pressure. This, of course, puts certain 




Fig. 230 



A Treatise on Milling and Milling Machines 245 




Fig. 231 




Fig. 232 



246 



The Cincinnati Milling Machine Company 



indentations in the work, but where these are not objectionable 
this form of clamping has much to commend it on the score of 
simplicity and strength. 

For Side Locations there are practically no standard con- 
structions. The usual practice is to press the work against flat or 

pointed screw heads. Sometimes 
it is desired to locate from some 
surface in conjunction with a boss. 
in which case flags may be utilized. 
The flag consists of a swinging 
member, the end of which termi- 
nates in a profile which agrees 
with the boss from which it is 
desired to locate. After the work 
has been chucked in the fixture 
the flag is swung into position 
over the boss, and the operator by 
means of various screws and 
clamps, wedges the work over 
until the flag and boss are in 
agreement. A good example of 
this is shown in Fig. 235. In other 
cases the location must be from 
the surface that is to be machined, 
so that the locating member must 
be removed before the cutter passes over the work. A comparatively 
simple way of doing this, shown in Fig. 236. entails the use of a 
bracket having either a formed locating piece or two screws which 
may be set in any desired plane. This bracket can be slid along the 
front of the fixture so that __ _____ 

the work having been lined 
up by it will be left free 
for the cutter when the 
bracket has been slid to 
the next piece, or out to 
the end of the fixture. 
There is with this con- 
struction, of course, the 
danger that the operator may forget to remove his locating piece. 
and for certain high-production jobs a method similar to that shown 
in Fig. 237 can be followed. 




Fig. 233 



TYCfiZK 




Fig. 234 



A Treatise on Milling and Milling Machines 247 

The fixture is so arranged that the side locating points are auto- 
matically removed from the path of the cutter by the advance of the 
table. The illustration shows the details of this construction. A 
pair of swing brackets, A, carrying the locating point proper, are 



Fig. 235 

No. 4 Plain Miller with tandem fixture and 12" diameter face mill, 26 revolutions, feeding 20" per 
minute, finishing the 13" x 11" surface of a cast-iron crank case in 2.6 minutes. 

caused to rotate around the pivot by the movement of the plungers 
B, which are in turn actuated by the cam C that is fastened 
to the stationary headstock. 

Setting Pieces are often used in milling fixtures to insure the 
proper relationship between the machined surface and some other 
rough or previously machined part. These setting pieces may be 
divided into those that are hardened and placed in such a position 
as to be entirely free from the action of the cutter, and those which 
are soft and can not be so placed. The first type is well illustrated 
in Fig. 238, which shows a large angle bracket fixture carrying a 
casting which is to be operated on by a comparatively complicated 
gang. On the face of this angle bracket and well removed from the 



248 



The Cincinnati Milling Machine Company 



cutters will be noted two hardened gauges. A, having one flat and 
one angular side. These correspond with the important surfaces 
to be machined. 

In setting up a job the cutters are placed on the arbor and the 
fixture brought up so that the cutters are between the setting points. 
pieces of tissue* paper being used to determine their proximity. The 
cutters being set in the proper relationship, the table is moved back 




1 



^ 



CCSTTF^5 



fevi?S 



1 







Fig. 256 

to the chucking position, the work inserted and the pieces all milled. 
It is possible for the operator to test the continued accuracy of 
alignment at any time by simply repeating this process. It is not,, 
of course, intended that he should do this for each piece. 

The other type of setting piece shown in Fig. 239 is based on the 
use of a soft steel piece, A, fastened to the end of the fixture and 
having stamped on its surface a dimension, which dimension is 
supposed to be measured by the toolkeeping department as soon as 
the fixture is turned in after use. If by any accident, the setting 

*In our own practice the gauges or setting points are made .010" undersize. 
and a .010" steel thickness gauge is used instead of tissue paper. 



A Treatise on Milling and Milling Machines 249 



piece has been damaged by the cutters, it is a simple matter to 
replace the same and to always secure exact duplication. (B is a 
swinging gauge for testing the piece before it is removed from the 
fixture.) 

This latter method is to be recommended more where the cutters 
are delicate and liable, on account of the nature of the job, to be 
brought in contact with the setting piece and also where the setting 
piece itself is comparatively difficult to reproduce as a hardened unit. 




Fig. 237 

Duplex Miller facing two ends of starter frames. Face mills 7H" diameter, 41 revolutions. Material, 
steel castings. Feed 4" per minute, quick forward and reverse 100" per minute. Accuracy for parallelism 
plus or minus .002". Time per piece 3H minutes. 

Simple Fixture for One Piece. Passing then to the more 
specific types of fixtures, we will first consider the simple fixture 
designed to hold one piece for use either on a Horizontal or Vertical 
Milling Machine, an adequate illustration being found in Fig. 240 
and detailed in Fig. 242. It will be noted that the work rests on 
three fixed screw heads and is supported at intervals by additional 
adjustable points. The supporting points and side clamping screws 
are all of the standard types described above and prove adequate 
to hold the work under a heavy roughing feed of 20" per minute. 
After the surfaces have been roughed and the side clamping screws 
slightly slackened up to release the bowing effect attendant on the 



250 



The Cincinnati Milling Machine Company 



side pressure, the finishing cut is taken at the same feed, resulting 
in a very flat surface with a degree of smoothness sufficient to meet 
the requirements. This fixture is of about as simple a construction 
as can be evolved for such a job as that illustrated. 

Tandem Fixtures, String Jigs. Following the simple fixture 
to hold one piece only, comes either two such fixtures set in tandem 



911 JfM f 


^^^"*"\ V ST- -m 
J Bl„ iM-i 




A i ^ 


L— — — 1— 


V 




L * V 


jtlg" 



Fig. 238 

Largest cutters 8" diameter, 35 revolutions. Cut 6J^' wide, &' deep. Feed 6H* per minute. Piece, 
cast iron, 18" long. Time for the cut 3J4 minutes. 

for either gang or reciprocal milling, or a string fixture which accom- 
plishes the same results. Fig. 243 illustrates such a fixture arranged 
to hold six pieces. In this case the work rests on two fixed points, 
A, and on two additional points, B, which are carried on each end 
of a lever so that the depression of one end of the lever results in an 
elevation of the other end and a consequent automatic lining up 
of all four support points in one plane. This does away with the 
need for individual adjustment of the fourth support point for each 
piece and is made possible largely by the rectangular shape of the 
piece and the even distribution of the cut. The details of this device 
are shown in Fig. 244. All three pieces at each end of the fixture 



A Treatise on Milling and Milling Machines 251 

are clamped by the one cam lever, C, which first brings over the 
clamp D nearest to the central fixed portion, E, of the fixture, 
following up with the closing of the second clamp, F, and finally 
with the end clamp, G, which it will be noted is made very much 
heavier than the intermediate clamps, since this end clamp must 




Fig. 239 

No. 2 Plain Cone-Driven Miller with string jig finishing steel machine parts \ z /i" long, Irs" wide 
at 73 feet cutting speed, .033" feed per revolution (3.1* per minute) in r 7 D minute each. 



take the whole of the feed pressure. It will be noted further that 
the arrangement of the clamps is such that their continued forward 
movement results in a downward pressure. This point must be 
continually watched and has been emphasized in axiom 5, page 233. 
Attention is also drawn to the provision for taking care of any lack 
of parallelism in the piece to be clamped. In Fig. 244 the details 
of the swinging clamp show that on one side it is provided with two 
gripping edges and on the other side with one edge only. The piece 
is therefore held between three points so that its lack of parallelism 
has no effect on the piece behind. The same result is sometimes 
obtained through side clamps of the construction shown in Fig. 233, 
which have their heel or fulcrum arranged so that an advance along 
the line of the clamp bolt is accomplished by a downward move- 
ment along the inclined plane. 



252 



The Cincinnati Milling Machine Company 



It is, of course, understood that either of the fixtures above 
described can be used equally well on a Vertical or Horizontal 
Machine and no attempt will be made in this chapter to differentiate 
between the use of different types of machines. 




Fig. 240 

No. 4 Vertical Miller milling the periphery of a rectangle 18 \i' x 26J4* without stopping either feed 
or speed, and without leaving an offset where the cut ends. Roughing cut ts' deep, feed 20* per minute. 
Finishing cut 20" per minute. Total cutting time 9 minutes. 



The first of the illustrations given above refers to a fixture that 
may be used either singly or in tandem with the feed pressure in the 
same direction. It can equally well be used for a reciprocating 
job, except that in such a case it would be desirable to put the fixed 
stop for receiving the cutter or feed thrust 
on the other side of the fixture so that 
the left-hand fixture when feeding towards 
the right would take the feed pressure on 
the solid stop on the left-hand end of the 
fixture and the right-hand fixture when 
feeding towards the left would take its 
thrust on the fixed stop located on the 
right-hand side. It will then be seen that 
with the exception of the location of the end stop, the fixtures for 
individual gang or reciprocal milling may be the same. 



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Fig. 241 



A Treatise on Milling and Milling Machines 253 



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254 The Cincinnati Milling Machine Company 

Loading Fixtures. In certain limited fields the loading fixture 
can be very advantageously employed. Particularly is this the 
case where the length of cut or time taken for the cut is extremely 
short, and where the chucking of the piece consumes a very large 
proportion of the total time. In such cases a pair of fixtures can be 
used, one of them being on the table of the milling machine, the 




Fig. 243 

No. 2 Plain Cone-Driven Miller with tandem multiple clamping fixture, milling aluminum magneto 
bases. Largest cutters 4J£" diameter, 236 revolutions, feed .071* (16%* per minute). Production 3 to 4 
pieces per minute. 

other on a convenient bench where either the operator or a helper 
can be removing the finished and inserting fresh, unfinished pieces. 
Fig. 245 shows an arrangement for milling spark plugs in which 
this method is utilized. There are two work holders, each provided 
with a number of collets for gripping an individual piece. The work 
holder proper takes care of 37 plugs. The plugs are chucked in the 
fixture which is lifted to the table, dropped over a locating pivot 
attached to the table and clamped with bolts sliding in the T slots. 
It is located accurately by means of a plunger fitting between the 
sides of the T slots and sliding in a bush carried in the fixture. The 
work is then milled, indexed through 60° by means of other bush- 
ings in which the plunger fits and then re-indexed, making three 



A Treatise on Milling and Milling Machines 255 



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256 



The Cincinnati Milling Machine Company 



passages in all, which completes the milling of all six sides of the 37 
plugs. The fixture is then released, lifted off the table, and the 
other fixture containing new plugs dropped in its place. The opera- 
tion is then repeated. With this arrangement the helper can be 
working all the time on the fixture that is off the milling machine 
table, and he can further be assisted by the machine operator in 
the intervals between reversing the feed, removing and inserting 




Fig. 245 

No. 2 Plain Cone-Driven Miller with loading fixtures, each holding 37 spark plugs. Three indexings 
of the fixtures complete the six sides of the plugs. One man and a helper produce three complete spark 
plugs per minute. 

the fixtures. For the successful operation of this method, reason- 
ably quick devices must be used for the clamping of the loading 
fixture to the table, cams and compressed air having been success- 
fully applied for this purpose. 

Right Angle or Square Fix- 
ture. In all of the above cases we 
only use the table feed of the machine 
in one direction with a consequent 
idle return stroke which may or may 
not be utilized to give a finishing 
cut. To eliminate this return stroke 
we can, where the work is small 
enough, use a right angle or square fixture as referred to in the 
comparison of methods previously made. Such a fixture as shown 
in Fig. 247 does away with any idle travel whatever and often will, 
from the point of view of production, compare favorably with the 
rotary method. 




Fig. 246 



A Treatise on Milling and Milling Machines 257 

In the fixture illustrated there are four compartments, the 
pieces being set as shown in the line cut, Fig. 248. All four pieces 
are milled by using a combination of table and cross feed. The 
methods of support are similar to those previously illustrated, the 




Fig. 247 

No. 3 Vertical Miller with right angle or square milling fixture. Pieces, cast iron, 5" x 1%". Cut 
iV deep. Cutter 6" diameter, 33 revolutions, feed \2 3 /i" per minute. Time per piece 39 seconds 

only notable points being the arrangement of the clamp, which it 
will be seen consists of a flat plate having trunnions which rotate in 
the fixture, being operated by a screw to which is attached per- 







Fig. 248 



Fig. 249 



manently a crank handle. The fulcrum of this plate, or clamp, 
is set back of the surface to be gripped so that the downward ten- 
dency is secured. The end of the screw operating these clamps is 



258 The Cincinnati Milling Machine Company 

turned down and provided with a screw head so that while the crank 
handle can easily be slipped off the square it can not be entirely 
removed from the screw and lost. This arrangement means that 
the operator can always set the crank handle in an easy position for 
gripping the work and still make allowance for variation in the 
thickness of the casting. 

Another point to be observed on this fixture is that all of the 
four handles for gripping the work are brought either to the front 
or side of the fixture. Such an arrangement is, of course, absolutely 
necessary if any kind of speed in clamping is to be maintained. 

One of the advantages of this type of fixture as compared with 
the rotary fixture, is that a more solid union is effected between the 
fixture and the milling machine, due to the abolition of the extra 
rotary attachment members. This method consequently lends 
itself rather more to those jobs that call for a reasonably heavy 
material removal in addition to a high production. 

Rotary or Continuous Milling Fixtures. The rotary method 
of milling gives a high rate of production on certain classes of 
work. This has been dealt with in the earlier chapter on Milling 
Methods and we now show in Fig. 250 a fixture designed for holding 
pole pieces while milling the base surface. The location of this 
piece is rendered simple since a previous grinding operation provides 
a finished surface on which the piece may be located. The only 
points to be watched then are the method of gripping and the dis- 
position of chips. For gripping the piece, reliance is placed on a 
central ring, this ring having a number of facets to correspond with 
the number of pieces held in the fixture. These facets are undercut 
at an angle which corresponds approximately with the curvature of 
the piece and they are additionally provided with file-cut surfaces 
which embed slightly into the surfaces of the pole piece and make a 
very efficient gripping device. The outer or movable gripping 
member is a cam provided with longitudinal serrations and pivoting 
around studs carried in the frame of the casting. The end of the 
cam projects in the form of a lever which is either tightened by hand 
or by blows from a lead hammer. The fixture itself is practically 
in two halves, the central half carrying the locating ring and the 
outer half carrying the gripping cams, these two halves being joined 
together by a series of ribs. In between these ribs the chips fall 
clear of the top surface of the Circular Attachment into a trough sur- 
rounding said attachment, from where they may be easily removed. 



A Treatise on Milling and Milling Machines 259 



The foregoing illustrations cover practically the full line of stand- 
ard methods of milling with face mills on both Horizontal and 
Vertical Machines. 

Reciprocal Fixtures. When it is desired to mill either 
one or two faces parallel to each other, the reciprocating 





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Fig. 250 

No. 2 Vertical Miller with continuous milling fixture holding 12 polepiece forgings, with surfaces 
2j^* x 3*. Cutter 4" diameter, 68 revolutions, feed 12%* per minute. Production 4 per minute. 

method is often used in conjunction with a gang of side 
mills. A good example of this is shown in Fig. 252, 
where a gang of four milling cutters machine at one passage two 
sides of two large hexagon nuts. To make the fixture comparatively 
universal, the studs on which the nuts 
(they have not been previously threaded) 
rest may be removed and substituted by 
other sizes. The nut is gripped to these 
studs by means of the two angular plates 
A, which move in slots BB, set at 
right angles to the surface to be gripped. 
These plates move downward through the 
right and left-hand screw D, operated Fi ^ 251 

by the crank handle C, shown on the right-hand side of the fix- 
ture. By this means two pieces are gripped with one movement 






_-: The Cincinnati Milling Machine Company 



of the lever and a wide range of sizes can be easily accommodated 
Willi the one fixture. There is nothing special to be noted in the 
construction of this other than the arrangement of the gripping 
pieces above described. 

An elaboration of this method is found in Fig. 253, which shows 
a pair of hand-indexed fixtures arranged for cutting slots in the 
flanges of automobile hubs. It is, of course, obvious that this 



r.£. ::: 

~EL il~ -• \\..' -vi :-.■:. ;::■::.. :r jr zzl zz.z :' l^zj^ziz. - -~J sicIl surface '. \ ' z I ' with 

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method leaves a curve at the bottom of the slot corresponding to 
the diameter of the cutter. The work is gripped by a contracting 
collet or split end of the spindle of the attachment, the circular 
surface of the work having been previously turned. Attention 
is irawn here to a device that should more often be applied to 
miffing fixtures; that is, the ejecting mechanism. It very often 
happens that a very well-designed fixture that is entirely satis- 
factory in every other point fails in that the closeness of fit between 
(he gripping device and the work renders it difficult for the operator 
to remove the piece without a certain amount of manual labor that 
ought to be avoided. In this fixture a lever is provided, located 
conveniently a: Hie rear of the fixture, which on being struck or 
pushed ejects (he work. The details of the indexing are not par- 
ticularly import::: and will be dealt with in that part of the chapter 
irTCTc-d :: inderiiz ±rrires. 



A Treatise on Milling and Milling Machines 261 



Automatic Releasing Fixtures. Following the hand ejecting 
of work, one naturally comes to the automatic releasing and ejection 
of same. Fig. 255 shows an equipment for holding magneto base 
plates while milling the tops and edges. The piece rests on three 
fixed supports and is clamped by the central plate A, having 
knife edges, said plate being attached solidly to the fixture. The 




in 



f"*1l< 



Fig. 253 

No. 3 High-Power Miller with reciprocal hand index fixtures finishing four slots 1" wide, 1" deep 
automobile hubs. Feeding i%" per minute, removing }/$" metal in 1.8 minutes per complete hub. 

gripping is through two levers, B, with their fulcrum to the rear 
of the gripped surface, the gripping being actuated by a balanced 
cam, which in turn is connected to the handle C projecting from 
the front of the fixture, the details of this mechanism being shown 
in Fig. 256. There is nothing particu- 
larly interesting about this part, but 
attention is drawn to the small lever 
D carrying the pin E shown pro- 
jecting from the rear of the fixture. 
This encounters a bracket fastened to 
the face of the column and when the 
table is returned either by hand, or as 
in this case, by the power quick return, 
to the starting point, the lever referred 
to, striking the bracket on the column, automatically throws open 
the gripping levers and permits of the work being removed without 
any releasing action on the operator's part. This fixture merely 
releases automatically and does not eject. 




Fig. 254 



262 



The Cincinnati Milling Machine Company 



Automatic Clamping, Releasing and Ejecting Fixtures. 

The fixture shown in Fig. 257 grips, releases and ejects automatically. 
It was designed for milling flats on the ends of terminals for storage 
batteries and is arranged with two inner rows of fixed V blocks. Op- 
posing these blocks are a series of movable V blocks carried on the 
ends of plungers which are held against the work by very heavy 




Fig. 255 

No. 2 Plain Cone-Driven Miller with automatic releasing fixture finishing six sides of aluminum 
castings 2%" x 33^* x ts' in two settings. Speed 225 revolutions, feed .020* (4J^* per minute). Time .57 
minute per piece. 



springs, the containers, or cartridges for these springs extending 
outside the fixture as seen in the illustration. Each of these movable 
V blocks is arranged to hold two pieces. Immediately beneath the 
extension of the fixture which carries the V blocks is a support which 
is attached to the headstock or tailstock of the machine and con- 
sequently does not move with the table. Attached to the head 
and tailstock of the machine is a cam (this being made in sections) 
which first imposes a relatively light pressure on the spring plungers 
and later, at that part immediately beneath the cutters imposes a 
sufficiently heavy pressure to hold the work against the cut. The 
cam terminates immediately at the back of the cutters. 



A Treatise on Milling and Milling Machines 263 

The pieces having been dropped into the V blocks rest on the 
stationary base and are carried along by the feed of the machine. 
As they approach the cutters the second portion of the cam grips 
them firmly while they pass under the cutters and after this they are 
entirely released. At this point the stationary base ends and the 
pieces which have hitherto been sliding along on this base drop 




SECTION THRU J\JK. 




Fig. 256 



out of the open V blocks into a chute which carries them away. 
At the conclusion of the stroke the table and fixture automatically 
return to the starting point; the operator loads up enough pieces 
to afford him a sufficient degree of safety, engages the table feed, 
and as the table moves forward, finishes loading up the fixture. 
This operation is, with the exception of the idle return, one of almost 
continuous production. 

To approach closer to the ideal condition would entail the use 
of a swinging or indexing fixture which would duplicate the details 
of the one illustrated, with this exception: that the work-holding 
portion would be split up into two halves, one on each side of a 
vertical axis. The stroke of the machine would be shortened to 
agree with only that number of pieces held in the one half of the 
fixture, so that the operator would be able to entirely load one end 
while those pieces in the other end were being milled. At the end 



264 The Cincinnati Milling Machine Company 



of the cut the fixture would be swung around 180° and the cut 
immediately started on the new pieces. This would reduce the idle 
time to approximately one-tenth of a minute per half cycle, which 
loss need hardly be considered. 

Hand Indexing Fixtures. Indexing, either hand or automatic 
can, of course, be applied to almost any type of fixture. The index- 
ing may be for any of the following purposes : 

a. To cut a number of faces or slots in a single piece. 

b. To provide means for milling both ends of a piece. 

c. To remove the loading and unloading position from too 
close proximity to the cutter, and 

d. To provide continuous cutting and loading. 

Fig. 258 shows a Clutch-Cutting Fixture that illustrates classi- 
fication a, in which a number of interesting features are found. 



till - - 111 

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Fig. 257 

Automatic Plain Miller fitted with automatic clamping, releasing and ejecting fixture, milling flats 
Y% high, -fa* deep, on bars 5 /% diameter. Cutting speed 315 feet. Feed 6" per minute. Accuracy within 
.0005". Production 11 pieces per minute. 

These are shown clearly in the drawing, Fig. 259. This fixture was 
designed for cutting the teeth in clutches of different sizes, which 
had a rather widely varying number of teeth. The clutches are 
held by means of an expanding collet, the expansion being secured 
through a taper-headed drawbolt A, which is engaged by the 
lever B, shown projecting from the lower center of the fixture. 
This lever carries a segment of a nut, which segment is thrown 



A Treatise on Milling and Milling Machines 265 

into engagement with the screw when the operator grips the second- 
ary handle C attached to the main handle. When the secondary- 
handle is released the segment immediately disengages itself from 
the screw, so that the work-carrying spindle can rotate, leaving 
the locking handle free. By this means the locking handle can 
always occupy the same convenient position in the front of the 
fixture so that the man does not have to hunt for it. Attached to 
the upper part of the work-carrying spindle is a removable index 
plate D, a number of these plates being provided to index 
different divisions. One of the plates for instance, has 24 teeth, 
so that clutches having 24, 12, 8, 6 or 4 teeth can be milled. The 
index plate is engaged with a long straight index pin E, which 
is connected to the camshaft, which is operated by the cam F, 
shown at the right-hand side of the fixture. This cam terminates 







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Fig. 258 

No. 2 Plain Cone-Driven Miller with indexing fixture milling 27 teeth -£%" deep into steel clutches 
at 230 feet cutting speed, .073' feed (21* per minute). Total time for milling and chucking complete lYi 
minutes each. 



in a handle which in turn carries a stop block G, that abuts the 
movable block H, that is clamped to the serrated segmental 
T slot I. Certain portions of the stroke of this cam are constant 
so that the degree of rotation required for withdrawing or releasing 
the plunger and for driving the plunger home again are not affected 
by the degree of rotation required to insure the proper angle of 
indexing. This result is obtained through a link connection between 



266 



The Cincinnati Milling Machine Company 



the cam proper and the stud S on which it rotates, so that the 
commencement of the withdrawal stroke and the conclusion of the 
locating stroke are unaccompanied by any rotation of said shaft. 
After the cam has been partially rotated and the plunger released, 
a continued movement of the cam will, through the pin N and slot 
P, cause a rotation of the shaft, but this without any rotation 
of the gears through which the work-carrying spindle is rotated. 




Fig. 259 



When the cam has been rotated as far back as the stop will permit 
and a return stroke commenced, the roller clutch J, which will be 
noted at the lower end of the cam-carrying shaft engaging with 
the gear K, which forms the roller clutch, causes, through the 
intermediate gear, a rotation of the index or work-carrying spindle. 
This spindle is then indexed through the required number of degrees 
and the conclusion of the cam stroke, forcing the index plunger home, 
effectively locks the work in the required position; in other words, 
a single lever moved first to the left and then to the right, unlocks 
and withdraws the index plunger, rotates the work and locks the 
index plunger home again within the required slot so that the 
operator works entirely independent of the sense of touch and sight 
and can with the greatest ease secure the desired indexing. 



A Treatise on Milling and Milling Machines 267 

The fixture is extremely low so that no undue twisting strains 
are imposed on the machine table and it is thoroughly protected 
against the bad effects of chips entering the indexing mechanism, 
this being effected through a cover which completely envelopes 
the outer part of the fixture. (The illustration, Fig. 258, was made 




Fig. 260 

High-Power Miller with triple spindle indexing fixture milling splined shafts 2H' diameter, 
18" long. Feed 3H ' per minute. Keys accurate within .001" ; diameter of shafts at bottom of keys, within 
.005". Time 18 minutes each. 



with this cover removed, but it is shown in place in Fig. 152, page 
164.) 

This principle can, of course, be equally well applied to a multi- 
spindle indexing fixture. 

Another type of Hand Indexing Fixture, in this case with three 
spindles, is shown in Fig. 260. Here all three spindles are indexed 
through the one lever which is attached to one of the index plates, 
A. However, to get accuracy in the indexing, individual index 
plates and plungers are fitted to each spindle, the withdrawing of 
the plunger and releasing of the same being effected through cams 
and loose gear connection between the three spindles. This arrange- 
ment has the advantage of giving accurate indexing, undisturbed 



268 



The Cincinnati Milling Machine Company 



by the inaccuracy of the gear transmission between spindles and 
also has the speed that comes with the use of a single indexing lever. 
The particular job for which this fixture was designed, is that of 
milling splines in gas tractor shafts. This method of milling such 
parts is not recommended where a high degree of accuracy is required, 
on account of the practical impossibility of getting all three cutters 




Fig. 261 

Automatic Plain Miller with parallel tandem hand index fixture roughing out SH'. 52-tooth, 6-pitch. 
\y% face, alloy steel ring gears with i}4' diameter cutters, ISO feet cutting speed in 13 minutes each. 



to be, first, of the same diameter, second, to all run true; and 
third, to be all pitched with perfect relationship to the centers 
of the work on which each one operates. For roughing out and for 
certain grades of work, however, it is perfectly feasible. 

It will be noted that with this fixture, supporting brackets were 
supplied in addition to the support given by the headstock and tail- 
stock. These brackets cany spring V blocks B, which have to 
be loosened and reset after each indexing, as otherwise the lack of 
straightness in the work would, of course, affect the accuracy of 
the slots and keys produced. 

Another Hand Indexing Fixture shown in Fig. 261 is designed to 
mill four bevel gears at one setting, arranged parallel in pairs, 
placed tandem. The fixture is to some extent universal in that the 
number of divisions can be varied, but the angle, of course, can 
only be changed through the insertion of taper shims A beneath 



A Treatise on Milling and Milling Machines 269 

each half of the fixture. The index arrangement which controls 
all four spindles is attached to the front end of the fixture and con- 
sists of a plunger fitting into a bush, which plunger is keyed to a 
gear through which motion is transmitted to the wormshaft which 
rotates the different work spindles. By providing a slot in which 
the bush can be moved, either to or from the center and by varying 
the gear ratio, it is, of course, possible to vary the angle of division 




Fig. 262 

No. 1 Plain Miller with automatic indexing fixture milling six slots in automobile hubs. Slots %" 
wide, %" deep. Cut from solid forgings in two minutes per hub, complete. 



and still use a complete turn of the index plunger for each tooth 
to be milled. 

This method of indexing has much to recommend it over the 
usual sector commonly applied on Dividing Heads and other indexing 
apparatus, since it eliminates entirely the danger of the operator 
inserting the plunger into the wrong hole, or accidentally opening 
up the space between the two legs of the 
sector. 

Automatic Indexing Fixtures. A good 
example of the first type of indexing fixture 
with automatic indexing is shown in Fig. 262, 
which is the same method as that used in the Fi e- 263 

Hand Indexing fixture, Fig. 253, and for almost identically the same 
piece. In this case, however, the fixture is automatically indexed 
through the power quick traverse of the machine. This indexing, 
which is through 60°, is accomplished through a bracket A fastened 




270 



The Cincinnati Milling Machine Company 



to the face of the column, carrying a cam shaft B which engages 
with a ratchet-controlled cam C which withdraws the plunger D. 
The plunger has one straight and one angular side and is lifted out 
of engagement with the slots in the index wheel E, through a 
movement of the cam in a clockwise direction caused by the traverse 
of the fixture away from the cutter. The returning of the table to 




Fig. 264 

Automatic Duplex Machine with double spindle automatic indexing fixture and gang of four cutters, 
roughing out 7-9-pitch, 33-tooth automobile transmission gears. Cutting speed 61 feet. Feed 8* per 
minute. Production 100 gears per ten-hour day. (Hoods have been raised to show cutters.) 



bring the work again in touch with the cutter causes a reverse 
action of the pawl, which has, of course, been sliding along over the 
teeth of the ratchet and this is accompanied through a ratchet 
clutch by a clockwise rotation of the index plate, and at the con- 
clusion of the stroke a release of the index pin, which, falling into 
the slot, takes care of the indexing. With certain slight variations 
this type of automatic indexing can be almost universally applied 
and is incorporated in most of the automatic index fixtures shown 
hereafter. 

Fig. 264 shows an Automatically Indexed Double Spindle Fixture 
for roughing out spur gears, and Fig. 265 shows the rear view of 
this same fixture and gives a clearer idea of the means provided to 
secure rotation of both spindles through the one stationary 



A Treatise on Milling and Milling Machines 271 



cam shaft A and the ratchets R, and also secure accurate indexing 
through the use of two plungers B and index plates C. Attention is 
also drawn to the use of four work arbors so that the operator can 
be loading up two of them while the machine is milling the pieces 
held in the other two. In this particular case gears have been 
roughed out with a maximum pitch variation of .001" which, of 













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Fig. 265 

course, would not be practical if the transmission from the first 
to the second work spindle through gearing was also the means for 
indexing the second spindle. 

Swiveling Fixtures. Illustrating class b type of indexing 
(swiveling) fixture we show Fig. 266, representing a fixture used 
for milling connecting rods. Two of these rods are held side by side, 
and since the width of the ends is not the same they are placed 
with the large end of one at the side of the small end of the other. 
By first feeding in, one large and one small end is milled. After swivel- 
ing the fixture 180° the operation is repeated and the remaining two 
ends are finished so that both rods are machined at one time, doing 
away with the danger attendant upon a second chucking and the 
consequent lack of alignment. The indexing tooth A carried in 
the base plate of the fixture is hinged at B, projects over the edge 



272 



The Cincinnati Milling Machine Company 



of the table and consequently can be placed low, thus reducing the 
total height of the fixture. For supporting the end of the connecting 
rod the angular adjustable support points (Fig. 228) are used and 
can be seen projecting from the left-hand side of the indexing plate 
at C. 




Fig. 266 

No. 3 Plain Cone-Driven Miller with sniveling fixture finishing ends of automobile connecting rods. 
Cutters 10" and 8" diameter, feed .068", speed 41 revolutions. Time, including chucking, 3 minutes per 
piece. 

Another simple type of hand indexing fixture shown in Fig. 268 
dispenses with the use of a base plate. There is on this particular 
operation no need for extreme accuracy of indexing. If the job were 
being handled in sufficient quantities to 
justify a special machine for this opera- 
tion it would without doubt be handled 
on an Automatic Duplex Miller. 
However, the quantities not warrant- 
ing this, the simple equipment shown 
proved eminently satisfactory. The 
base plate to which the cylinder is 
clamped is bored out in the center to 
receive a stud, the lower part of this 
stud being flat to fit the T slot in the table. This stud is then 
clamped to the table by a bolt passing through its center and the 




A Treatise on Milling and Milling Machines 273 

fixture is dropped over the stud, rotating around it on the table 
surface. For indexing, a plunger A is used, which plunger is 
simply slid by hand along the same T slot of the table in which 
the pivoting stud is fastened. It is necessary to release the four 
bolts B that hold the fixture to the table and slide them and 
the indexing tooth out of engagement with the base of the fixture, 




Fig. 268 

No. 4 Cone-Driven Miller with swivel jig finishing bosses on engine cylinders. Cutter 6' diameter, 
60 revolutions, .300" feed, cut y% deep. Time, both sides, including chucking, 15 minutes. 

after which the fixture may be swung around and the bolts and 
index tooth reinserted. There are, of course, objections to this 
method of indexing; first, the impossibility of adequately guarding 
the top of the table from chips and the consequent scratching and 
grooving of same; second, the lack of accuracy due to the im- 
possibility of securing a proper and permanent sliding fit between 
the index tooth and the sliding table; and third, the time consumed 
in the indexing operation. One big advantage to be found from 
this construction is the great rigidity that results from clamping the 
fixture directly to the table. 

Where it is desired to secure a combination of rapid indexing 
and at the same time great rigidity of clamping, there are very few 



274 



The Cincinnati Milling Machine Company 



better methods than that used in the fixture shown in Figs. 269, 
270, 271. This is a fixture designed to hold a piece of considerable 
height which was subjected to a very heavy hammering or inter- 
mittent cut. imposing great strains on the locking mechanism of 
the fixture. It was also necessary to get great accuracy of indexing 
between the two extreme positions, which positions were used when 
milling the angular surfaces of a piece, a section of which is shown 




: 







i 


-X 
JTT] 1 


— 


_ BLOCK. 






=L p_ =jp 




E 






i 




ZTTTP^i 


liiij im 


^ a 


i 













Fig. 269 



at A. To accomplish these results the indexing was made through 
a pair of hardened plungers being brought into contact with similar 
hardened plungers in a block fastened to the stationary portion of 
the fixture B. These plungers, which were set up solid when in 
final position, also were arranged so that adjustment could be made 
by the toolmaker when assembling the fixture. To insure perfect 
contact between the fixed and indexing plungers, cam C was used, 
this cam being mounted on the bracket or fixed plunger support, 
and so being self-contained as far as the strains set up in insuring 
this contact were concerned. By this means the danger of a close 
and hard, alternating with a light and easy, contact were overcome. 
The indexing mechanism was, therefore, made to serve but one func- 
tion, that of indexing, and had no connection with the rotating 



A Treatise on Milling and Milling Machines 275 



mechanism, which takes the form of a semi-circular dovetail slide 
D, rotating around a corresponding complete dovetail E in 
the base plate. (Fig. 270.) Entering into and forming the other 
half of the bearing or dovetail is a dovetail slide F, Fig. 269, which 
is forced forward and released by means of the cam G, shown at 
the rear. The effect of the angularity of the sliding member and 
the angularity of the circular dovetail portion is to pull the rotating 
member firmly on to its seating over its full surface, which ar- 



h 



-2^- 




Fig. 270 

rangement can hardly be accomplished by any combination of 
horizontal and vertical locking mechanisms, since in this design the 
horizontal and vertical adjustments are made simultaneously. An 
unusual rigidity in the locking mechanism and unusual mainte- 
nance in correct bearing is secured with this construction, which 
can be strongly recommended for work where accuracy and long life 
are desired. 

Separation of Swiveling from Indexing Functions. It is 

always particularly desirable in accurate indexing mechanisms to 
separate those parts which are responsible for the entirely different 
functions of swiveling and indexing. A comparatively simple and 
extremely rigid indexing fixture is that shown in Fig. 272. This 
fixture was designed for cutting grooves either straight or angular 
in cutter blanks. When cutting the straight grooves the fixture 
was mounted directly on the table of the machine and when cutting 
angular grooves on an angled raising block A, as shown in the 



276 



The Cincinnati Milling Machine Company 



illustration. The interesting features of this fixture are the extremely 
liberal index teeth and the arrangement of the index plunger. The 
details of this are shown in Fig. 273. It will be noted that the index 
plunger proper is a separate piece of hardened steel fastened to a 




-__-__- ^— --y — r ^s^~ — *-M~^ i 

. 1 r* TT • T3r < oca > Y'-^ttttttttttz 



iX-*- ft%"f ' •*-£'* 



Fig. 271 



pivoting member B. the pivot being placed so that it is as nearly 
as possible in a line perpendicular to the straight side of the index 
tooth and starting from the end of that tooth. With this arrange- 
ment it is impossible to cause engagement between the tooth and 
index slot until the index plate shall have rotated past the desired 
position. The driving home of the index tooth, therefore, causes 
sliding action between the angular surfaces of the index tooth and 



A Treatise on Milling and Milling Machines 277 

slot and brings the straight sides of these members together with- 
out any sliding friction and consequent wear. As a result the 
accuracy of indexing is much more permanent than when this little 
point is neglected. It can, of course, be easily seen that if wear is 
permitted to take place indiscriminately on both sides of the index 
plunger and is not confined to the one unimportant nonaligning 




Fig. 272 

No. 3 High-Power Miller with hand index fixture cutting 20 slots y<f wide, V/2 deep, into a 12* diameter 
steel face mill body 2Y<£ thick, at two cuts, feeding 2" per minute in 78 minutes per body complete. 



side we will have much less certainty as to the accuracy of the 
indexing than when such precautions are observed. For driving 
the index plunger home a cam C is used, this consisting of a disc 
having a flat milled on it and having a hole bored eccentric to the 
circular contour. This is a very simple construction and gives not 
only a powerful lock but also a quick release and is done without any 
elaborate cam construction. In place of the usual arrangement for 
pulling out the index pin which, as a rule, consists of a spiral spring 
in tension anchored to some convenient part of the fixture, A spiral 



27S 



The Cincinnati Milling Machine Company 



spring in compression is used, this spring being let one-half into 
the fixture and one-half into the index plunger or pivoting plate. 
The details of this are clearly shown in the drawing and it is recom- 
mended as a very convenient and satisfactory spring arrangement 
in that the spring can be given a small travel with less likelihood of 
permanent set and at the same time is thoroughly concealed and 




* CPK 



31 



*L. 



.U-5"i-\ 







Fig. r: 



guarded from injury either in use or transit from the machine to 
the toolroom. 

The foregoing description covers most of the standard milling 
fixture construction. It can not do more than indicate the different 
types and it must not be understood that these standard Types wi'd 
cover all classes of milling. 

For even." individual job a different set of conditions arise, 
demanding a separate study. The proper designs for fixture and 
cutter are essential if the milling machine is to be an efficient tool. 
Lacking these, there is but little chance for any satisfactory results 
to follow its installation. 



A Treatise on Milling and Milling Machines 279 



CHAPTER XIV 

THE SIZING AND GUTTING OF 
SPUR GEARS 

If two smoothly turned rolls are mounted on parallel shafts 
with their surfaces in close contact, as shown in Fig. 274, and one is 
turned through an arc, then the other will also revolve. If the 
circumferences of the end faces are divided into equal parts, and 
at the start two division lines are placed opposite each other, then, 
as we turn, the other division lines will come in line with each other. 
In other words, the circumference of the driven roll moves as many 
inches as the circumference of the driver. If the driver has 6" 
circumference and the driven 12 ", then it takes two entire turns of 
the driver to bring the driven roll around once. We see, therefore, 
the number of turns of the two rolls are in inverse ratio to their 

circumferences, and consequently 
to their diameters. This is, of 
course, only theoretically true, as 
in actual practice there would be 
slippage. 

To prevent slippage both rolls 
are provided with teeth. It would 
not be safe to provide roll A alone 
with teeth on the outside, as these teeth would have no place to go un- 
less we cut corresponding grooves into roll B. To make all such re- 
volving parts of similar construction, we provide them with teeth 
above and grooves below their friction surfaces. Although the friction 
surface itself has then disappeared entirely, it remains the most im- 
portant factor in the design of such parts. The diameters of these two 
friction surfaces determine the ratio of the number of revolutions 
of these rolls. 

Rolls with teeth are called gear wheels. When the rolls are cylin- 
ders, as shown, the gear wheels are called spur gears. The original 
friction surfaces are called pitch surfaces or pitch cylinders. A 
section of the pitch surface at right angles to the axis is called a 
pitch circle, or more generally the pitch line. 




280 The Cincinnati Milling Machine Company 

As there is no slippage possible between the teeth of these wheels, 
our rule now becomes absolutely fixed. The relative number of revo- 
lutions of two mating spur gears is in inverse ratio to their pitch 
circumferences, and consequently to their pitch diameters. 

In order to get a smooth uniform action of one gear on the other, 
the teeth must be of a certain definite shape. It is possible to make 
the teeth of one of the rolls of almost any shape, provided the teeth 
of the mating roll are shaped to suit. It is desirable, however, to 
make gear wheels in such a way that a given wheel can run with 
many others and not solely with the one with which it is mated, 
because in many mechanisms gear wheels must be interchangeable. 
The experience of a great many years has gradually limited the shapes 
of gear teeth to only one system; namely, the involute shape of 
tooth. 

Circular Pitch. If the rolls shown in Fig. 274 were provided 
with a tooth at every point where a mark appears, the distance 
between these marks would be called the pitch of the gear wheel. 
We say, therefore, that: 

The pitch of a gear wheel is the distance from center to center 
of two adjoining teeth, measured along the pitch circle. This pitch is 
called the CIRCULAR PITCH. 

Chordal Pitch. Years ago, when practically all gear wheels 
were cast and when the patternmaker had to construct the gear 
wheel, he used his dividers to space the teeth of his pattern. The 
dividers were set to the length of the chord and not the arc, between 
the centers of two adjoining teeth. This distance was therefore 
called "chordal pitch." This chordal pitch is not used in metal gear 
cutting and will not be considered here. 

Diametral Pitch. When the diameter of a circle is an even 

number of inches, or some simple fraction, the circumference of 

that circle becomes a decimal fraction which never expresses exactly 

the length of the circumference, however many decimals we might 

use. If the diameter is 1", then the circumference is 3.1415926535. 

Of course it would not be practical to use all these figures, nor would 

it be practical to work to such a degree of accuracy, and therefore 

the circumference of the 1" circle is often expressed by 3.1416, and 

sometimes even by 3.14. There are also common fractions which 

22 
express the length of the circumference very closely, such as, — 



A Treatise on Milling and Milling Machines 281 

355 

for ordinary work, and for more accurate work. In either case 

113 

the circumference is an odd fraction when the diameter is a simple 

figure or fraction, and vice versa, the diameter would be an odd 

figure if the circumference were an even figure. The use of circular 

pitches, therefore, leads to awkward fractions when computing a 

set of gears. To simplify the matter, Diametral Pitch has been 

uniformly adopted. This makes it easy to determine any factor in 

the design of a gear when some of the others are known, as for 

instance, to find the number of teeth when diameter and pitch are 

given, and so on. 

The diametral pitch is a number expressing how many teeth 
there would be in a gear of 1" pitch diameter. 

If, for instance, the diametral pitch is 10, then a gear V pitch di- 
ameter would have 10 teeth, a gear 2" pitch diameter would have 
2 x 10 = 20 teeth. This 2" diameter gear would have 2 x 12 teeth if the 
pitch were 12, and 2 x 16 teeth if the pitch were 16, and so on. From 
these simple data we derive the following rules: 

To find the number of teeth of a gear, multiply the diametral pitch 
by the pitch diameter. 

To find the pitch diameter of a gear, divide the number of teeth by 
the diametral pitch. 

To find the diametral pitch of a gear, divide the number of teeth 
by the pitch diameter. 

To find the center distance of two mating gears, divide half the 
sum of their teeth by the diametral pitch. 

To find the sum of the numbers of teeth of two mating gears, multiply 
their center distance by the diametral pitch and multiply this product 
by 2. 

In all that follows, "Pitch" is understood to be the Diametral 
Pitch, unless otherwise designated. It will be represented by the 
letter P. Circular Pitch by P. 

Addendum and Dedendum. It is not only necessary to have 
a certain standardized shape of the gear teeth if we want the gears 
to be interchangeable, but it is also necessary that all gears of the 
same pitch should have the teeth project the same fixed height above 
the pitch surface and the grooves the same fixed depth below. A 
number of considerations enter into this matter and there has been 
established a definite relation between these dimensions of the 



282 The Cincinnati Milling Machine Company 

teeth and the pitch. The system most common at the present time 
makes the height of the gear tooth above the pitch line (pitch sur- 
face equal to 1 divided by the pitch. For a 5-pitch gear this height 
would be i". For a 10-pitch gear it would be iV, etc. This is 
called the addendum. 

The depth of the tooth below the pitch surface is made equal to 
the height above the surface. This is called the dedendum. If 
gears were actually made this way they would have to be absolutely 
perfect and their center distance would have to be absolutely cor- 
rect, otherwise the top of a tooth might interfere with the bottom 
of a groove of the mating gear. For that reason the grooves are cut 
somewhat deeper than this theoretical depth. This additional 
depth is called clearance. The sum of addendum and dedendum 
is called working depth. The difference between working depth 
and the full depth is called clearance. 

Outside Diameter.* If we have a gear of 20 teeth, 10 pitch, 

20 

then its pitch diameter is — = 2". The addendum of such a gear 

1 10 

would be — and, as this addendum is added to the radius of the 

gear, the outside diameter of this gear will be 2.2". This outside 
diameter is the same as the pitch diameter of a gear of 22 teeth, 
10 pitch, so that we find the following rules: 

The outside diameter of a gear is found by adding 2 to the number 

of teeth, and then dividing it by the pitch. 

The number of teeth of a gear is found by multiplying the outside 
diameter by the pitch and then subtracting 2. 

Circular Pitch, Clearance and Full Depth. We have seen 
that a gear 1" pitch diameter, 10 pitch, has 10 teeth. Such a gear 
would have a pitch circumference of 3.1416, so that the circular 
pitch of this gear would be 3.1416 divided by 10 = .31416. 

*lf there are two mating gears on a pair of shafts, and there should 
also be another pair of gears on these shafts opposite each other, but which must 
clear each other, then the outside diameters of these gears added together 
must be somewhat smaller than the sum of the pitch diameters of the mating 
gears. In other words, the sum of the numbers of teeth of the two gears which 
must clear each other must be at least four less than the sum of the numbers of 
teeth of the mating gears. As the slightest error in the size of the mating gears, 
or the center distance, would cause the other gears to interfere, it is customary 
to either make the sum of their numbers of teeth five less than that of the mating 
gears, or else turn them down a slight amount. 



A Treatise on Milling and Milling Machines 283 



To find the circular pitch, divide 3.11+16 by the diametral pitch. 

It is customary to make the clearance at the bottom of the teeth 
equal to ^o of the circular pitch. The total depth of a tooth 
being composed of the addendum, dedendum and clearance, is 
found as follows: 

Since the circular pitch equals — - — then 2V of the circular 

pitch = — x — = that is . 157 divided by the pitch. 

P 20 P 

Since the 

Addendum = 1 divided by the pitch = — 

Dedendum = 1 divided by the pitch = — 

157 

Clearance = . 157 divided by the pitch = 

We have by adding these 

1 1 .157 2.157 , , , ., 

1 1 = = whole depth. 

P P P P 

From the above we deduce these rules: 

The whole depth is 2.157 divided by the pitch. 
The clearance is 0.157 divided by the pitch. 

Pressure Angles. Fig. 275 shows a pair of teeth of two mating 
gears in such a position that a point on the pitch circle of one gear 
is pressing on a point of the pitch circle of the mating gear. The 
direction of this pressure depends on the shape of the teeth. The 
most common form of tooth 
used at the present time is such 
that the direction of the pres- " 
sure AB makes an angle 143^ 
degrees with the tangent com- 
mon to the pitch circles at this 

point. This line AB in the direction of the pressure is called the line of 
action. In later years many builders of machinery have adopted a sys- 




284 The Cincinnati Milling Machine Company 

tern of gearing by which this line of action makes an angle of 20 de- 
grees with the common tangent. It was formerly thought that such an 
angle of 20 degrees would cause too much pressure on the bearings, 
too much wear on the gear teeth and a less smooth action between 
the gears, but recent thorough investigation has shown that this is 
not so. It has been found, on the other hand, that the teeth are 
stronger, the pressure on the bearings is not perceptibly more, the 
action is as smooth, and the wear on the teeth is not greater. 

A rack belonging to the system of gears which has an angle of 
action of 14 y 2 degrees, has teeth with straight sides which make 
an angle of 14 3^ degrees with the vertical. When the angle of action 
is 20 degrees, the rack teeth will also be straight, but make an angle 
of 20 degrees with the vertical. 

Not all makers of gear wheels make the addendum and dedendum 
as indicated above. Sometimes the teeth are made shorter and are 
called stub teeth. These, however, will not be discussed here. 

It is customary to make the tooth and the space equal in width, 
therefore the thickness of the tooth on the pitch line equals half 
the pitch. 

Selecting the Cutter. The shape of the tooth changes with the 
number of teeth of the gear, so that the exact shape of a tooth of 
a gear with 179 teeth is different from the proper shape for a 180- 
tooth gear. The difference would be extremely small in this case, 
but it would be somewhat greater for gears of 20 and 21 teeth respec- 
tively. This difference in shape becomes more marked in gears with 
the smaller number of teeth. For most practical purposes these varia- 
tions can be ignored to a certain extent. It is common prac- 
tice to cut gears with any number of teeth, but, of course, all 
of the same pitch, with eight different shapes of teeth, so 
that a set of only eight cutters is required for one pitch to cut any 
gear from 12 teeth up to a rack. The eight cutters adopted are: 

No. 1 to cut a wheel from 135 teeth to a rack. 
No. 2 to cut a wheel from 55 teeth to 134 teeth. 
No. 3 to cut a wheel from 35 teeth to 54 teeth. 
No. 4 to cut a wheel from 26 teeth to 34 teeth. 
No. 5 to cut a wheel from 21 teeth to 25 teeth. 



A Treatise on Milling and Milling Machines 285 

No. 6 to cut a wheel from 17 teeth to 20 teeth. 
No. 7 to cut a wheel from 14 teeth to 16 teeth. 
No. 8 to cut a wheel from 12 teeth to 13 teeth. 

These eight cutters are made with the correct shape for the lowest 
number of teeth which they are supposed to cut. If then, we want 
to cut a gear with 48 teeth we must select the No. 3 cutter, which 
will cut gears of from 35 to 54 teeth, but we know that the 
shape of the tooth will not be entirely correct. The shape thus pro- 
duced will be found sufficiently accurate in a large number of cases 
where high speeds and great smoothness of running are not essential. 
However, if gears must be cut very accurate, then it becomes neces- 
sary to use a special cutter made to the correct shape for that par- 
ticular number of teeth. Cutter makers are prepared to furnish 
such cutters. 

Cutting Gears on the Milling Machine. Until within the 
last few years, practically all cut gears were made by means of a 
rotary milling cutter of such a shape as to produce the correct 
shape of teeth. Now, many gears are made by the process of nob- 
bing or shaping. In this discussion we are concerned only with the 
process of milling the teeth. Ordinarily, gear wheels are milled on 
automatic gear-cutting machines, which are specially designed for 
this one class of work. However, the installation of a gear cutter 
may not be advisable in a shop that has not much gear cutting to 
do. In such cases this work is done on the milling machine. A 
milling machine will cut the teeth as rapidly as a gear cutter, and 
it does not take longer to set up the milling machine than the gear 
cutter. Aside from having an indexing worm wheel of large di- 
ameter, the only advantage it has over the milling machine is that it 
automatically indexes the gear and returns the cutter at a rapid 
rate. The gear cutter then does not require any further attention 
after a job has once been started, whereas the milling machine 
requires the attention of an operator for indexing and advancing 
the work and throwing in the feed. This, however, does not amount 
to anything where only one or a few gears of a kind have to be cut 
at one time, so that, even in shops where there are gear cutters, 
odd jobs of gear cutting are frequently done on the milling machine, 
because this machine lends itself to rapid setting up and no par- 
ticular preparation for indexing is required. Fig. 276 shows the 
milling machine in operation milling a spur gear. 



286 The Cincinnati Milling Machine Company 



Setting the Machine. When setting up the machine for 
cutting a spur gear, care should be taken to see to it that the machine 
is in correct adjustment in every respect, all as discussed on pages 
65-66 in the paragraphs on the use of the Dividing Head. It is of the 
utmost importance that the cutter be kept sharp. This is discussed 
in detail in Chapter X, on Cutter Sharpening. A properly sharpened 




Fig. 276 

Cutting a spur geax on the Milling Machine. The gear is held between centers in the nBual way. 

cutter should be mounted on the arbor as close to the end of the 
spindle as permissible, and it may be well to use an intermediate 
support as in Fig. 276 to give additional stiffness to the arbor. 

Now, adjust the table so as to bring the dividing head center 
up close to the cutter and then make transverse adjustments to 
bring the dividing head center to coincide exactly with the center 
of the face of the tooth of the cutter. Since gear cutters are 
provided with a central line on the outside of their teeth this can be 
very easily done by simply bringing the dividing head center to 
coincide with this line on the cutter. We can now lower the table, 



A Treatise on Milling and Milling Machines 287 



place our piece of work between centers and properly secure it by 
means of a dog to the driver, making sure that there will be no 
chance for back lash. 

The index pin must be set to the proper circle of holes as deter- 
mined from the index tables; the plate itself must be securely locked, 
making sure that there is no back lash at this point; the index pin 
should be brought around in the direction in which the indexing 
will be done, which is preferably in the direction of the hands of a 
clock and allowed to drop into one of the holes. Then set the 
sector for the proper spacing; tighten the spindle clamp at the rear 
of the dividing head ; start the machine; raise the work up carefully 
until the revolving cutter begins to show the first slight evidence of 
touching the work; then set the elevating dial to zero, run the table 
to the right clear of the cutter and then raise up the required amount 
for the proper depth, all of which may be read from the dial; dis- 
engage the elevating crank so as to reduce the possibility of the 
adjustment being dis- 
turbed, and now we are 
ready to proceed with 
the milling. 

Cutting La rge 
Gears. It sometimes 
happens that the milling 
machine is called upon 
to cut gears which are so 
large in diameter that 
they can not pass be- 
tween the table in its 
lowest position and the 
cutter on the arbor. 
Such work can be done 
in two different ways. 

First, by using the Un- 
dercutting Attachment, 
described on page 25. 
This attachment makes 
it possible to cut gears 
of large dimensions and coarse pitches on machines of moderate size. 

Second, by setting the spindle of the Dividing Head in a vertical 
position as shown in Fig. 271. It will be quite clear that by holding 




Fig. 277 

Cutting a large spur gear on the Milling Machine by set- 
ting the dividing head spindle vertical and using the up feed. 



288 



The Cincinnati Milling Machine Company 



the work in this position a very large gear can be accommodated, 
but instead of using the longitudinal table feed we must now use 
the vertical feed, and we should feed up so that the pressure of the 
cutter on the work will be down towards the table. This makes it 
comparatively simple to place a supporting rest under the rim of 
the gear as close as possible to where the cut is being taken. It 
must of course be remembered that although the dividing head is 
made to a close degree of accuracy, nevertheless, as the gears grow 
larger the index errors which do exist will be correspondingly multi- 
plied. However, these methods make it possible to cut very satis- 
factory gears whenever an occasional odd size gear must be cut. 

Table of Tooth Parts 







Whole 


Thickness 




Working 


Diametral 


Circular 


Depth of 


at 


Addendum 


Depth of 


Pitch 


Pitch 


Tooth 


Pitch Line 




Tooth 


1M 


2.5133 


1.726 


1.257 


.8000 


1.600 


IK 


2.094 


1.438 


1.047 


.6666 


1.333 


\% 


1.795 


1.233 


.898 


.5714 


1 . 1429 


2 


1.570 


1 078 


.785 


.5000 


1.000 


2M 


1.396 


.959 


.698 


4444 


.888 


2^ 


1.256 


.863 


.628 


.4000 


.800 


2% 


1.142 


.784 


.571 


.3636 


.727 


3 


1.047 


.719 


.524 


.3333 


.666 


3K 


.897 


.616 


.449 


.2857 


.571 


4 


.785 


.539 


.393 


.2500 


.500 


5 


.628 


.431 


.314 


.2000 


.400 


6 


.523 


.360 


.262 


.1666 


.333 


7 


.448 


.308 


.224 


.1429 


.285 


8 


.392 


.270 


.196 


.1250 


.250 


9 


.349 


.240 


.175 


.1111 


.222 


10 


.314 


.216 


.157 


.1000 


.200 


11 


.285 


.196 


.143 


.0909 


.181 


12 


.261 


.180 


.131 


.0833 


.166 


14 


.224 


.154 


.112 


.0714 


.142 


16 


.196 


.135 


.098 


.0625 


.125 


18 


.174 


.120 


.087 


.0555 


.111 


20 


.157 


.108 


.079 


.0500 


.100 


22 


.142 


.098 


.071 


.0455 


.090 


24 


.130 


.090 


.065 


.0417 


.083 


26 


.120 


.083 


.060 


.0385 


.076 


28 


.112 


.077 


.056 


.0357 


.071 


30 


.104 


.072 


.052 


.0333 


.066 


32 


.098 


.067 


.049 


.0312 


.062 



The "whole depth of tooth" is the depth to be cut in gear. 



A Treatise on Milling and Milling Machines 289 



Rules and Formulas for Dimensions of 
Spur Gears 

For the sake of convenience the useful rules that can be deduced 
from the foregoing discussion of spur gears, together with their 
formulas, are given on the following pages. In view of the fact that 
practically all the gear problems arising in the machine shop are based 
on the use of diametral pitch, we have tabulated the rules and formu- 
las for diametral pitch by themselves and give in a supplementary 
table similar rules and formulas for circular pitch for use when such 
gears are to be made. We believe this separation of the data for diam- 
etral pitch from those for circular pitch will avoid the confusion that 
sometimes arises when they are all placed in one table. 



In these tables the following notation is used : 



P 

P' 

N 



= diametral pitch. D = 

= circular pitch. C = 

= number of teeth; (if the num- S = 

ber of teeth in both gear and F = 

pinion are referred to, Ng = W = 

number of teeth in gear, and T = 

Np = number of teeth in O = 
pinion). 



pitch diameter, 
center distance, 
addendum, 
clearance. 

whole depth of tooth, 
thickness of tooth, 
outside diameter of gear. 



circular pitch 




Fig. 278. Gear Tooth Parts 

The circular pitch is defined as the distance from center to center of two adjacent teeth along the 
pitch circle. The diametral pitch is a number found by dividing the number of teeth by the pitch diam- 
eter. In other words, it gives the number of teeth for each inch of pitch diameter. 



290 



The Cincinnati Milling Machine Company 



Rules and Formulas for Dimensions of Spur Gears Made to 
DIAMETRAL PITCH 



To Find 


Rule 




Formula 


Diametral 
Pitch 


Divide number of teeth by pitch diameter. 


P 


N 
D 




Number of 
Teeth 


Multiply pitch diameter by diametral 
pitch 


N 


= P 


X D 


Number of 
Teeth 


Multiply the outside diameter by the 
pitch and subtract 2 





X P 


- 2 


Total Number 
of Teeth in a 
Pair of Gears 


Multiply the center distance by the diame- 
tral pitch times 2 


c 


X P 


X 2 


Pitch 
Diameter 


Subtract two times the addendum from 
outside diameter 


D 


= 


- 2 S 


Pitch 
Diameter 


Divide number of teeth by diametral pitch. 


D 


N 
P 




Outside 
Diameter 


Add two times the addendum to the pitch 
diameter 





= D 


+ 2 S 


Outside 
Diameter 


Add 2 to the number of teeth and divide 
the sum by diametral pitch 





N 


+ 2 
P 








Whole Depth 
of Tooth 


Divide 2 . 157 by diametral pitch 


w 


2 


157 
P 


Addendum 


Divide 1 by diametral pitch 


s 


1 
P 




Dedendum 


Divide 1 by diametral pitch 


1 
p 












Clearance 


Divide 0. 157 by diametral pitch 


F 


0. 


157 


j 


P 


Thickness 
of Tooth 


Divide 1. 5708 by diametral pitch 


T 


1. 


5708 




P 


Center 
Distance 


Add the number of teeth in both gears and 
divide the sum by two times the diame- 
tral pitch 


C 


Ng + Np 




2 P 








Center 
Distance 


Divide the sum of the pitch diameters of 
a pair of gears by 2 


D 


+ D 






2 




Length of 
Rack 


Multiply number of teeth in rack by 3.1416 
and divide by diametral pitch 


L 


3. 


1416 N 






P 



A Treatise on Milling and Milling Machines 291 



Rules and Formulas for Dimensions of Spur Gears Made to 
CIRCULAR PITCH 


To Find 


Rule 


Formula 


Diametral 
Pitch 


Divide 3 . 1416 by circular pitch 


P 


3.1416 






P' 


Circular 
Pitch 


Divide 3 . 1416 by diametral pitch 


P' 


3.1416 
P 


Pitch 
Diameter 


Multiply number of teeth by circular pitch 
and divide the product by 3 . 1416 


D 


NP' 
3.1416 


Center 
Distance 


Multiply the sum of the number of teeth in 
both gears by circular pitch and divide 
the product by 6 . 2832 


C = 


(Ng + Np)P' 
6.2832 


Addendum 


Divide circular pitch by 3 . 1416 


s 


P' 
3.1416 


Clearance 


Divide circular pitch by 20 


F 


P' 






20 


Whole Depth 
of Tooth 


Multiply . 6866 by circular pitch 


W 


= 0.6866 P' 


Thickness 
of Tooth 


Divide circular pitch by 2 


T 


P' 
2 


Outside 
Diameter 


Multiply the sum of the number of teeth 
plus 2 by circular pitch and divide the 
product by 3 . 1416 





(N + 2) P' 
3.1416 










Multiply pitch diameter by 3.1416 
divide by number of teeth 


and 


P 


3. 1416 D 


Pitch 


N 








Pitch 
Diameter 


Subtract two times the addendum J 
outside diameter 


Torn 


D 


= - 2 S 








Number of 
Teeth 


Multiply pitch diameter by 3.1416 
divide the product by circular pitch 


and 


N 


3. 1416 D 
P' 


Outside 
Diameter 


Add two times the addendum to the pitch 
diameter 





= D + 2 S 








Length of 
Rack 


Multiply the number of teeth in the rack 
by circular pitch 


L 


= NP' 



292 



The Cincinnati Milling Machine Company 



Comparative Table of Circular and Diametral Pitch 

Table No. 1 shows the diametral pitches with the corresponding 
circular pitches. 

Table No. 2 shows the circular pitches with the corresponding 
diametral pitches. 



Table No. 1 


Table No. 2 


Diametral Pitch 


Circular Pitch 


Circular Pitch 


Diametral Pitch 


2 


1.571 in. 


2 in. 


1.571 


W± 


1.396 


m 


1 676 


2M 


1.257 


m 


1.795 


2% 


1.142 


m 


1.933 


3 


1.047 


V4 


2.094 


m. 


.898 


l£ 


2.185 


4 


.785 


m 


2.285 


5 


.628 


1A 


2.394 


6 


.524 


IK 


2.513 


7 


.449 


1A 


2.646 


8 


.393 


IVs 


2.793 


9 


.349 


1^ 


2.957 


10 


.314 


l 


3 . 142 


11 


.286 


15 
16 


3.351 


12 


.262 


Vs 


3.590 


14 


.224 


13 
16 


3.867 


16 


.196 


H 


4.189 


18 


.175 


11 
16 


4.570 


20 


.157 


Vs 


5.027 


22 


.143 


9 
16 


5 . 585 


24 


.131 


V2 


6.283 


26 


.121 


7 
16 


7.181 


28 


.112 


Vs 


8.378 


30 


.105 


5 
16 


10.053 


32 


.098 


H 


12.566 


36 


.087 


3 

16 


16.755 


40 


.079 


Vs 


25.133 


48 


.065 


i 

16 


50.266 



Metric or Module System of Gear Teeth. The metric sys- 
tem of measurement does not use diametral pitches., but instead, 
the dimensions of gear teeth are expressed by reference to the 
module of the gear. The module is equal to the pitch diameter in 



A Treatise on Milling and Milling Machines 293 



millimeters divided by the number of teeth in the gear. For example, 
if the pitch diameter of a gear is 50 millimeters and the number of 
teeth 25, then the module equals 50 ^- 25 = 2. The accompanying 
table gives a comparison between diametral, circular and metric 
pitches, together with their decimal equivalents. To convert 
module or metric (for example M 2) into the equivalent diametral 
pitch, proceed as follows: 

M 2 = .247", or in other words, it is the same as a circular pitch 
of .247". 



P = 



3.1416 



P' in Inches 



P= 3 1 141_6 = 12 
.247 



Comparative Table of Diametral, Metric and Circular Pitches 

with Decimal Equivalents 

Number of Teeth 3.1416 
Diametral Pitch, P = = 



Module = 



Pitch Diameter in Inches Circular Pitch in Inches 
Pitch Diameter in Millimeters Circular Pitch in Millimeters 



Number of Teeth 3.1416 

Pitch Diameter in Inches X 3.1416 
Circular Pitch, P' = 



3.1416 



Number of Teeth 



Diametral Pitch in Inches 



Dia- 
me- 
tral 
Pitch 


Mod- 
ule 


Cir- 
cular 
Pitch 


Deci- 
mal 
Equi- 
valent 


Dia- 
me- 
tral 
Pitch 


Mod- 
ule 


Cir- 
cular 
Pitch 


Deci- 
mal 
Equi- 
valent 


Dia- 
me- 
tral 
Pitch 


Mod- 
ule 


Cir- 
cular 
Pitch 


Deci- 
mal 
Equi- 
valent 


26 






.121 
.124 
.125 
.131 
.143 
.155 
.156 
.157 
.175 
.185 
.187 
.196 
.216 
.219 
.224 
.247 
.250 
.262 
.278 
.281 
.286 
.309 
.312 
.314 




2M 


ii 

32 


.340 
.344 
.349 
.371 
.375 
.393 
.433 
.437 
.449 
.495 
.500 
.524 
.556 
.562 
.571 
.618 
.625 
.628 
.680 
.687 
.698 
.742 
.750 
.785 




7 


A 


.866 




1 


y% 


.875 




9 




SA 




.898 


24 




3 


N 


8 


l 


.989 


22 






1.000 




IK 


5 

32 


8 




3 




1.047 




zy 2 


7 
16 


9 


lA 


1.113 


20 




1.125 


18 






7 




2M 




1.142 




lA 


3 
16 


4 


A 


10 


IK 


1.237 
1.250 


16 




6 




2A 




1.257 




l% 


7 
32 


±A 


9 
16 


11 


m 


1.360 
1.375 


14 




5A 




2H 




1.396 




2 


K 


5 


5 A 


12 


IA 


1.484 
1.500 


12 




5 




2 




1.571 




2M 


9 

32 


$A 


ii 

16 


14 


"in 


1.732 
1.750 


11 




m 




IK 




1.795 




2V 2 


5 
16 


6 


H 


16 


2 


1.979 
2.000 


10 




4 




IK 




2.094 



294 



The Cincinnati Milling Machine Company 



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A Treatise on Milling and Milling Machines 295 





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296 



The Cincinnati Milling Machine Company 



Table for Cutting Racks — Continued 

(Using the Cross Screw for making divisions.) 



Pitch 
2 


Pitch 
2M 


Pitch 

2^ 


Pitch 
2% 


Pitch 
3 


Pitch 


Pitch 
4 


Pitch 
5 


> 


02 


o3 

CO 

O 
-d 

H 


> 

PS 


W2 

rd 

d 

o3 

CO 

d 
o 
-d 
H 


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a; 


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,d 

d 

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02 

d 
o 
A 
H 


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A 
-t-3 

d 

o3 

03 

d 
o 
A 
H 


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03 


02 

-d 

d 

o3 

d 
o 
,d 
H 


> 

03 


02 

A 

■+3 

d 

o3 

02 

d 
o 
pd 

H 


> 

03 


02 

A 
■+J 

d 

o3 

o> 

d 
o 
A 
H 


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03 


02 

fH 

d 

o3 

02 

d 
o 
,d 
H 


7 

7 
7 
7 
7 
7 
7 
7 
7 
7 


171 

142 

113 

84 

55 

26 

197 

168 

139 

110 


6 
6 
6 
6 
6 
6 
6 
6 
6 
6 


196 
192 
188 
184 
180 
176 
172 
168 
164 
160 


6 
6 
6 
6 
6 
6 
6 
6 
6 
6 


57 
114 
171 

28 

85 
142 
199 

56 
113 
170 


5 
5 
5 
5 
5 
5 
5 
5 
5 
5 


142 

84 

26 

168 

110 

52 

194 

136 

78 

20 


5 
5 
5 
5 
5 
5 
5 
5 
5 
5 


47 

94 

141 

188 

35 

82 

129 

176 

23 

70 


4 
4 
4 
4 
4 
4 
4 
4 
4 
4 


98 
196 

94 
192 

90 
188 

86 
184 

82 
180 


3 
3 
. 3 
3 
3 
3 
3 
3 
3 
3 


185 

170 

155 

140 

125 

110 

95 

80 

65 

50 


3 
3 
3 
3 
3 
3 
3 
3 
3 
3 


28 

56 

84 

112 

140 

168 

196 

24 

52 

80 



Pitch 
6 


Pitch 

7 


Pitch 

8 


Pitch 
9 


Pitch 
10 


Pitch 
11 


Pitch 
12 


Pitch 
14 


> 

03 


02 

rd 

+3 

d 

o3 

02 

d 
o 

rd 

H 


> 

03 


02 

,£3 
-(-=> 

d 

03 

02 

d 
o 
-d 
H 


> 


02 
rd 

d 

o3 

02 

d 
o 
-d 
H 


> 

03 


02 
c-j 

-^> 

d 

03 

CO 

d 
o 
A 
H 


> 

03 


02 
r\ 

d 

03 

02 

d 
o 
A 
H 


> 

03 


02 

£3 
-^> 

d 

o3 

02 

d 
o 

rd 


> 

03 


02 

£3 

+3 

d 

o3 

02 

d 
o 
^3 

H 


> 

03 
P4 


OJ 

A 

d 

03 

02 

d 
o 

rd 

H 


2 
2 
2 
2 
2 
2 
2 
2 
2 
2 


124 

48 
172 

96 

20 
144 

68 
192 
116 

40 


2 
2 
2 
2 
2 
2 
2 
2 
2 
2 


49 

98 

147 

196 

45 

94 

143 

192 

41 

90 




193 
186 
179 
172 
165 
158 
151 
144 
137 
130 




149 

98 

47 

196 

145 

94 

43 

192 

141 

90 




114 

28 
142 

56 
170 

84 
198 
112 

26 
140 




86 
172 

58 
144 

30 

116 

2 

88 

174 

60 




62 
124 
186 

48 
110 
172 

34 

96 
158 

20 




24 

48 

72 

96 

120 

144 

168 

192 

16 

40 



A Treatise on Milling and Milling Machines 297 



Table for Cutting Racks— Continued 

(Using the Cross Screw for making divisions.) 



Pitch 


Pitch 


Pitch 


Pitch 


Pitch 


Pitch 


Pitch 


Pitch 


Pitch 


Pitch 


Pitcli 


Pitch 


16 


18 


20 


22 


24 


26 


28 


30 


32 


36 


40 


48 


m 


co 


co 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


-fi 


j3 


A 


JZ 


-fi 


,£5 


X! 


JC 


X! 


X 


X 


M 


-u 


-♦j 


+j 


■*^ 


-^ 


-*j 


•+J 


-t-> 


+j 


-t-J 


-^ 


■+2 


TJ 


T3 


-3 


T3 


T3 


T3 


TS 


T3 


T3 


T3 


T3 


T3 


a 


C 


d 


a 


S 


fl 


a 


a 


CI 


£5 


CI 


a 


o3 


03 


03 


<a 


a3 


c3 


03 


a 


03 


03 


03 


o3 


m 


co 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


CO 


3 


a 


3 


3 


3 


3 


3 


3 


d 


d 


d 


p 


O 


o 


O 


c 


O 


O 


O 


O 


o 


o 


o 


O 


-G 


J3 


Si 


-C. 


J3 


J 


X 


-d 


J3 


x 


J5 


X! 


H 


H 


H 


H 


H 


H 


H 


h 


H 


H 


H 


H 


196 


175 


157 


143 


131 


121 


112 


105 


98 


87 


79 


65 


192 


150 


114 


86 


62 


42 


24 


10 


196 


174 


158 


130 


188 


125 


71 


29 


193 


163 


136 


115 


94 


61 


37 


195 


184 


100 


28 


172 


124 


84 


48 


20 


192 


148 


116 


60 


180 


75 


185 


115 


55 


5 


160 


125 


90 


35 


195 


125 


176 


50 


142 


58 


186 


126 


72 


30 


188 


122 


74 


190 


172 


25 


99 


1 


117 


47 


184 


135 


86 


9 


153 


55 


168 





56 


144 


48 


168 


96 


40 


184 


96 


32 


120 


164 


175 


13 


87 


179 


89 


8 


145 


82 


183 


111 


185 


160 


150 


170 


30 


110 


10 


120 


50 


180 


70 


190 


50 



Directions. — For example: To cut a 16-pitch rack, adjust the 
work to the cutter and set the micrometer dial of cross screw to 
zero. For the next tooth turn the cross screw crank until the mi- 
crometer reads 196 thousandths; for the following tooth continue to 
turn until the reading is 192 thousandths; and so on until you reach 
the last number in the above table; then without moving the cross 
screw set the micrometer dial to zero, and commence over again, con- 
tinuing as before. For cases in which one or more revolutions are 
required, make the number of revolutions and the necessary num- 
ber of thousandths beyond for each tooth, as shown in the table. 
For example : To cut a 3-pitch rack. Adjust the work to the cutter 
and set the micrometer dial on the cross screw to zero. Then mill 
the first tooth. For the next tooth, turn the cross screw crank 
through five complete revolutions, plus an additional amount until 
the micrometer dial reads 47 thousandths. When this tooth has 
been cut, index for the next tooth by turning the cross screw crank 
through five complete revolutions again and continue until the 
micrometer dial reads 94 thousandths. For the next spacing make 
five revolutions of the crank and continue around until the microm- 
eter dial reads 141 thousandths, and so on. 



298 



The Cincinnati Milling Machine Company 



Indexing Table for Use in Connection with Rack Indexing 
Attachment for Cone-Driven Millers 



Diametral 


Circular 


Diame- 


Gear 


Gear on 


Turns of 


Cir- 


Gear 


Gear on 


Turns of 


tral 


on 


Crank 


Index 


cular 


on 


Crank 


Index 


Pitch 


Stud 


Shaft 


Plate 


Pitch 

3 
i 


Stud 


Shaft 


Plate 


4 


88 


28 


Whole 


84 


28 


Whole 


5 


88 


35 


Whole 


11 
16 


77 


28 


Whole 


6 


88 


42 


Whole 


5 
8 


70 


28 


Whole 


7 


88 


49 


Whole 


9 
16 


63 


28 


Whole 


8 


88 


56 


Whole 


1 
2 


56 


28 


Whole 


9 


88 


63 


Whole 


7 
16 


98 


56 


Whole 


10 


88 


70 


Whole 


2 


56 


35 


Whole 


11 


88 


77 


Whole 


8 


84 


56 


Whole 


12 


88 


84 


Whole 


1 
3 


56 


42 


Whole 


13 


88 


91 


Whole 


5 
16 


70 


56 


Whole 


14 


88 


98 


Whole 


2 


56 


49 


Whole 


15 


88 


105 


Whole 


1 


84 


42 


Half 


16 


44 


56 


Whole 


! 


56 


70 


Whole 


18 


88 


63 


Half 


3 

16 


42 


.56 


Whole 


20 


88 


70 


Half 


1 
6 


56 


84 


Whole 


22 


88 


77 


Half 


1 
7* 


56 


98 


Whole 


24 


88 


84 


Half 


1 

8 


28 


56 


Whole 


26 


88 


91 


Half 


1 
16 


2S 


56 


Half 


28 


88 


98 


Half 










30 


88 


105 


Half 










32 


44 


56 


Half 











Indexing Table for Use in Connection with Rack Indexing Attachment 
for All Millers of High-Power Design 



Diametral 


Circular 


Diame- 


Gear 


Gear on 


Turns of 


Cir- 


Gear 


Gear on 


Turns of 


tral 


on 


Crank 


Index 


cular 


on 


Crank 


Index 


Pitch 


Stud 


Shaft 


Plate 


Pitch 


Stud 


Shaft 


Plate 


4 


88 


56 


Whole 


3 


84 


56 


Whole 


5 


88 


70 


Whole 


11 

16 


77 


56 


Whole 


6 


44 


42 


Whole 


5 

8 


70 


56 


Whole 


7 


44 


49 


Whole 


9 
16 


63 


56 


Whole 


8 


44 


56 


Whole 


1 
g 


88 


44 


Half 


9 


44 


63 


Whole 


7 
16 


49 


56 


Whole 


10 


44 


70 


Whole 


2 


56 


70 


Whole 


11 


44 


77 


Whole 


3 

8 


42 


56 


Whole 


12 


44 


84 


Whole 


1 
3 


56 


42 


Half 


13 


44 


91 


Whole 


S 
16 


70 


56 


Half 


14 


44 


98 


Whole 


2 

7 


56 


49 


Half 


15 


44 


105 


Whole 


1 


42 


84 


Whole 


16 


33 


84 


Whole 


1 


56 


70 


Half 


18 


44 


63 


Half 


3 
16 


42 


56 


Half 


20 


44 


70 


Half 


1 
6 


56 


84 


Half 


22 


44 


77 


Half 


1 
7 


56 


98 


Half 


24 


44 


84 


Half 


1 
8 


42 


84 


Half 


26 


44 


91 


Half 










28 


44 


98 


Half 










30 


44 


105 


Half 










32 


33 


84 


Half 











A Treatise on Milling and Milling Machines 299 



CHAPTER XV 
SHOP TRIGONOMETRY— BEVEL GEARS 

The name Trigonometry has a formidable sound to those who 
have had no special training in this branch of mathematics, but 
whose work frequently requires them to use it in their everyday 
shop work. It is intended here to cover only enough ground, and 
that in simple language, to enable anyone with a knowledge of 
arithmetic to solve the ordinary shop problems involving angles, 
and we have, therefore, headed this chapter Shop Trigonometry. 
This word is composed of two other words, which translated in their 
proper order mean — triangle measurement. In other words, trigo- 
nometry is simply the measurement of triangles. 

The basis of all the computations is the circle, which, as we all 
know, is divided into 360 divisions called degrees. 

1 degree = 60 minutes. 
1 minute = 60 seconds. 

In all mathematical calculations, the following symbols are 
used: 

° = degrees, thus 3 degrees = 3° 
' = minutes, thus 5 minutes = 5' 
" = seconds, thus 12 seconds = 12 " 

which is written 3°5'12", and reads "three degrees, five minutes, 
twelve seconds." 

The Right Angle Triangle. Of all the different triangles we 
can make the right angle triangle lends itself best to simple calcu- 
lations by means of trigonometry. 

One of the first things to be remembered is that the sum of the 
three angles of a triangle is 180°. A right angle triangle is a triangle, 
one of whose angles is a right angle. If one of the angles of a triangle 
is a right angle, or 90°, then the sum of the other two angles must 
also be 90°, because the sum of all the angles is 180°. 

From this we always know that one angle of the right angle 
triangle is 90°. If we know a second angle it is an easy matter to 



The Cd«3d*sia3i Mhjldog Machine Compasiy 



figllTr . ... 7 . ... J 1 

- - : " : - .. _ -. _ ' 



~: 






~ -".. 







"_£ 



DEL 

Z I - : 
-- irs 
changed so ubbng as we do 

■ -sry zoniplet© tables ha 
between AC and BC I car ai 
this proportion may be dim 
for still another seven-c^fr 
If you kn: ~ : .:. 2 : I . is 1 : ' 
rally want to kn c vr r_. = - - ... . 
I: 7: j. ^irr. :i__i ;::;•: rT;:i 
and fir: ::.:r. ■ ii ::t ^:r^ 
tion is .4^5i, you ifmiliiply 1 
of AC. If yoaa do not know 
instead, know : :. T 5 _: T ; : : r -5 
what the proportion is for I 

figUTf TI'.t SIZj-5 2i I»5f:r'T 

angle is just as good as fcno 
the table. Iff yon know :i- 
angle B is, you can, off cone 

5,2. ~r. t 2i 1 . r 



A Treatise on Milling and Milling Machines 301 

These tables not only give you the proportion between AC and 
BC when you know the angle B, but they also give you the pro- 
portion between AB and BC. They also give you the proportions 
between AB, AC, between AC, AB, between BC, BA and between 
BC, AC. Six of these proportions are given in the table, and a 
single multiplication will give you at once any of the sides of a 
right angle triangle if any of the other sides is given, or if you know 
one of the angles. 

Definitions of Sine, Tangent, etc.* Trigonometry would not 
seem so formidable if its terms were given in English instead of 
Greek and Latin words. "Measuring triangles" sounds much 
simpler than "Trigonometry," but it means the same thing. We 
find in the tables the terms: Sine, Cosine, Tangent, Cotangent, 
Secant and Cosecant. These words do not describe anything that 





Fig. 280 



Fig. 281 



*It has been customary to teach trigonometry by showing the angle 
as made by two radii of a circle in which the length of the radius = 1" (see Fig. 
280). It is possible to show angle AOB by the two radii CO and AO. If we drop 
the perpendicular CD on the line AO, and if we further assume that the radius 
OC of the circle is 1" in length, then the line CD is the sine of the angle COD, 
and OD is the cosine of this angle. If we erect a perpendicular at the point A, 
then this line will intersect the extension of the radius OC at the point B. In 
this case the radius AO is 1" in length, and the line AB is the tangent of the 
angle AOB. In the same manner the line EF is the cotangent of the angle AOB. 
These lines are tangents to the circle, and their length is determined by the 
points where these tangents intersect the legs of the given angle. This is the 
reason why the proportions mentioned are called the tangent and cotangent 
of the given angle. 

In Fig. 281 the radius OG is again 1", and the intersecting line, or secant, 
HG, is as many inches long as the value of the secant of the angle OGH. 



302 The Cincinnati Milling Machine Company 

we are familiar with in everyday life and they do not mean any- 
thing to us because we do not understand them. They can, how- 
ever, be readily translated into their English equivalents, which are 
words that we are familiar with, and the whole matter at once 
becomes simpler. 

Sine originally meant the string of a bow, or the chord of an arc 
of a circle, and in its present use in trigonometry, the angle sub- 
tended by that arc; therefore, so far as we are concerned, "sine" 
means simply "angle." What we find in the table under the heading 
Sine, is simply the proportion between two sides of the triangle 
for a given sine or angle. 

Cosine. — We saw above that if one angle is 30° the other angle 
must be 90° - 30° = 60°. These angles of 30° and 60° are said to 
be each other's complement; so are 10° and 80°; so are 17° and 73°. 
When the sum of any two angles is 90°, they are complementary 
angles. Therefore, in a right angle triangle the angles at B and C 
(Fig. 279) are always complementary angles. 

Cosine is an abbreviation or contraction for "complement sine," 
and simply means the sine of the complement angle. For instance, 
the Cosine of 30° is the same as the Sine of 60°; the Cosine of 10° 
is the Sine of 80° and, of course, vice versa, the Cosine of 60° is the 
Sine of 30°, and the Cosine of 80° is the Sine of 10°, and so on. 

Tangent, a word which you also find in the table, means just 
exactly what tangent has always meant to you: a line which 
touches a circle at one point. 

Cotangent simply means "complement tangent," or the tangent 
of the complement angle, so that the Cotangent of 30° is the Tangent 
of 60° and vice versa. 

Secant means a line which intersects a circle. You will recognize 
the same root in the words "secant" and "intersect." Cosecant means 
again the "complement secant" or secant of the complement angle. 

Trigonometry Expressed as Proportion. After this short 

explanation we are ready to proceed. The proportion between AC and 

BC, Fig. 279, can be, and in mathematical equations is, written 

AC AC 8 1 

— . If BC is 16 and AC is 8, then — = — = — , which is in exact 

BC BC 16 2 



A Treatise on Milling and Milling Machines 303 



accordance with our first assumption. In the triangle ABC, 



AC 
BC 



is the Sine of the angle B. The Sine and the Tangent are the two 
terms which are most used and we want to emphasize here that for 
both these terms we must always look to that side of the triangle 
which is opposite the given angle. If we have the angle B, then 
we must look for line AC. This is the Sine of the angle B and is a 
fraction of which the line opposite the angle B is the numerator 
and the hypotenuse is the denominator. The Sine of angle B is 



therefore 



AC 
BC" 



If we have the angle C we must look for the line 



AB. The Sine of angle C is therefore 



AB 
BC' 



The only difference in the fractions which represent the Sine 
and the Tangent of an angle lies in the denominator of the fraction. 
For the Sine this denominator is the hypotenuse, but for the Tangent 
it is the other right angle side, so that the Tangent of angle B is 

— and the Cotangent is — . 
AB AC 



Sine B equals — 



Cosine B equals 



Tangent B equals 



AC 
BC 



AB 
BC 

AC 
AB 



Cotangent B equals 



Secant B equals 



Cosecant B equals 



AB 
AC 

BC_ 
AB 

BC 
AC 



It will be seen that the Cosecant is the inverted value of the 
Sine, the Secant is the inverted value of the Cosine, and the Cotan- 
gent is the inverted value of the Tangent. In other words, the sine 
multiplied by the cosecant equals 1; and similarly, the tangent 
multiplied by the cotangent equals 1; and the secant multiplied 
by the cosine equals 1. This is not merely a curiosity, but it can be 



304 The Cincinnati Milling Machine Company 

made a great help in the calculations, as it enables us to multiply 
instead of divide, and it is much easier to multiply by a large number 
than to divide by it. If, for instance, we find that we have to divide 
by the sine of a certain angle, it is advisable to not do it, but instead, 
find in the tables the cosecant of the same angle and multiply by it. 

Another one of the properties of these values worth noticing is 
that we can find without referring to the tables some of these values, 
if some others are known. For instance, if we know the sine and 
cosine, we can find the tangent and all the other values, thus: 



AC 
sin B BC AC 



cos B AB AB 
BC 



= tan B 



similarly 



AB 
cos B BC AB 
sin B ~ AC " AC 

BC 



= cotan B, and so on. 



If we want to make free use of trigonometry there is just one 
thing that we must do: Learn by heart the tabulation given above, 
and learn it so that we know it as well as the alphabet or the multi- 
plication table. Outside of this there is nothing to be learned for 
right angle triangles except some practice in handling the tables. 
This practice will come only by doing the thing and doing it often. 

How to Use Trigonometric Tables. If in Fig. 279 angle 
ABC is 30°, what is the value of its sine? 

Referring to the table of sines and cosines, etc., page 428 in 
the column headed 30°, under the word sine, opposite 0, we find 
.50000, which means than sin 30°0' = .50000 or y 2 . That is exactly 

AC 

what we found to be the value of the proposition — in our first as- 

AB 

sumption when AC = 8 and AB = 16. 

Now suppose our angle is 30°19': We follow down the sine 
column under 30° and find opposite 19, at the left hand margin 



A Treatise on Milling and Milling Machines 305 

OF the table, the value .50478. Therefore, we know that sin 
30°19' = .50478. 

If we are seeking the value of the cosine we simply follow the 
above instructions, but look for our values in the column headed 
cosine, thus, cos 30°19' = .86325. In exactly the same way we 
can pick out of the table, the tangent secant and all the other 
functions. 

However, it will be seen that the tables go only as far as 44°60', 
and we may want the function of an angle somewhere between 45° 
and 90°. 

It was shown previously that the cosine is the same as the sine of 
the complementary angle, the cotangent is the tangent of the comple- 
mentary angle, etc. This fact has been taken advantage of in pre- 
paring the tables. Therefore, when we want the function of an 
angle larger than 45°, we read up; example, sine 46°22', on the bot- 
tom of the table page 400 we see 46°; the columns above this are 
designated cosine, sine, etc. Following up the sine column we find 
the value opposite the figure 22 at the right-hand margin of 
the table is .72377. Therefore, sin 46°22' = .72377, and so on. 

Bevel Gears: Application to a Shop Problem. To show how 
simple calculations are when carried out by trigonometry, we will 
calculate all the elements of a pair of bevel gears,* which run at 

*Bevel gears are gears which connect shafts, the axes of which intersect 
each other. The point of intersection is called the apex. If we should locate 
a wire at the apex and make it follow the outline of the bevel gear, this wire 
would describe a cone. Part of this cone is the bevel gear. A bevel gear may 
therefore be considered as a truncated cone. If we place ourselves behind the 
bevel gear cone it will appear to us as a circle. If we cut a pair of bevel gears 
through their axes the section will appear as in Fig. 282. O is the apex of both 
gears. The circle we would see when looking at the small gear cone would be 
the circle with AB as radius. This would be the pitch circle of the small gear. 

Bevel gears might be considered as being cut out of a sphere. We might 
imagine ourselves placed in the center of the sphere, and from there cut out 
sectors by means of a wire moving in a circle. Each sector would be the cone 
out of which we can make a bevel gear. If two sectors touch each other, then 
we have two bevel gears which will work together. Such a section of the sphere 
would appear on the outside of that sphere as a circle. These circles might 
be of various sizes, and the largest circle we could possibly get on that sphere 
would be the circle lying in a plane going through its center. Such a circle is 
commonly called a great circle of that sphere. If such a great circle is 
used as the pitch circle of a bevel gear, the gear is called a crown gear. If we 



306 The Cincinnati Milling Machine Company 

right angles to each other and of which only the number of teeth 
and pitch are given. Fig. 252 shows these bevel gears in section. 

The large gear has 42 teeth, the small gear has 19 teeth, both 
5 pitch. We will first calculate the pitch angle, or. as it is sometimes 
called,, the cone angle. The pitch angle for the pinion is AOB and 
for the gear AOC. Notice that in triangle AOB. AB is half the 
pitch diameter of the pinion, and OB. being equal to AC. is half the 
pitch diameter of the gear. We find the tangent of the angle AOB 
by dividing AB by OB. We really do not have to figure out AB and 
OB to do this; all we need to do is to divide the number o: teeth 
of the gear into the number of teeth of the pinion, but as we wish to 
know the diameters of the gears anyhow, we will overlook this 
little short cut. 

mi. si- u -r 4r * +u • number of teeth 42 c .„ 
The pitch diameter of the gear is = — = bA . 

pitch 5 



Half this diameter,, or the radius, is 4.2". The pitch diameter of the 

19 
5 



19 
pinion is — = 3.8". Its radius is half as much, or 1.9". The tansent 



1 9 

o: anz.e AOB is — — . V^ e see a: once that tne answer won. a nave 
4.2 

been the same if we had divided the number of teeth of the gear into 
the number of teeth of the pinion. This tangent we find to be 

should take a section through two bevel gears which work at right angles to 
each other, then we would get a right angle triangle. Fig. 282 shows such a 
triangle. The diameter AP of the small gear is one right angle side, the fiame- 
ter AQ of the other gear is the other right angle side, and the line PQ is the 
hypotenuse. This line PQ would be the diameter of A great circle of the 
sphere and would, therefore, be the diameter of the crown gear. 

As with spur gears, so it has been deemed advisable to select a system of 
tooth shapes by which gears which are cut out of one and the same sphere will 
properly run together. The system selected is that by which the teeth of a 
crown gear have straight sides like rack teeth in a spur gear system. Based on 
this peculiarity is a system of cutting bevel gears by means of a generating 
machine and a tool having the shape of a rack tooth. Such a generating machine, 
operating with such a tool, will produce a theoretically correct bevel gear. Rela- 
tively few shops possess a bevel gear generating machine, and therefore, cut 
such gears with a rotary cutter as when done on a milling machine. 



A Treatise on Milling and Milling Machines 307 

.45238, and we find from the table that the angle must be 24°20'. 
We might calculate the angle AOC in the same way by dividing the 
radius of the pinion into the radius of the gear, and this would give 
the tangent of the angle AOC, but this is not necessary, because 
the angles AOB and AOC together make 90° and are therefore 




complements of each other, so that if angle AOB is 24°20 / , the angle 
AOC must be what there is left of the right angle, or 90° - 24°20' 
= 65°40'. 

For many purposes, though not for all, it is desirable to know 
the line AO, which is called the pitch cone radius. Looking 

AO 
again at angle AOB, we see that — is the cosecant of AOB. If, 

AB 

therefore, we wish to find the line AO, we must multiply AB by 
the cosecant of angle AOB. We proceed thus: 



308 The Cincinnati Milling Machine Company 

AB x cosec AOB = AO. Substituting our values, we get 1.9 
x cosec 24°20' = AO. 

From the tables we find cosec 24°20' = 2.4269. We then have 
1.9 x 2.4269 = 4.61111. The length of AO is therefore 4.61111". 

From the chapter on cutting spur gears we see that the line AF, 
which is the height of tooth above the pitch line and is called the 

addendum, is 1 divided by the pitch, — ; in this case i. This 

is also the value of the line AG, the addendum of the pinion. 

Since the addendum and dedendum are equal and since their 
sum is the working depth, we see that the line FG is the working 
depth of both gear and pinion. The space between this working 

0.157 0.157 



depth and the whole depth is the clearance = 



5 



.0314 and since AF = AG = dedendum = — = — = .2 we find 

P 5 

that AH = AK = .2 + .0314 = .2314". This is the depth of the 
tooth below the pitch line. The whole depth, that is, the depth 
to be cut in the gear is the above + the addendum, or .2314 + .2 
= .4314". 

However, what we are really after is the angle AOK, as well as 
the angle AOH. Of course these two angles are alike. We are also 
interested in the angles AOG and AOF, which are also alike. If we 
once have these angles it will be a simple matter to find the angle 
FOC, which is the turning angle for the gear and HOC, which is the 
cutting angle for the gear; and it will be just as easy to find the angle 
GOB, the turning angle for the pinion and KOB, the cutting angle 
for the pinion. 

To find the angle AOG: We already know the length of the 
lines AG and AO in this triangle. Dividing one into the other we 

AO 
get the proportion = cotan AOG. 

* AG 

AO = 4.61111 = 23 Q555 = cotan AQG 

AG .2 

therefore, by consulting the tables we find AOG = 2°29', and AOF 
= 2°29' also. 



A Treatise on Milling and Milling Machines 309 

In the same way: 

CotanAOH = ^ = 4 - 61111 = 19.927, 
AH .2314 

therefore, AOH - 2°53' and AOK = 2°53' also. 

The turning angle for the pinion is, therefore, the pitch cone 
angle AOB + the angle AOG, that is, 

24°20' + 2°29' = 26°49 r 

and the cutting angle of the pinion is AOB - AOK, that is, 

24°20' - 2°53 / = 21°27'. 

In the same way by using the angle AOC of the gear, we find 
the turning and cutting angles of the gear. Turning angle of gear 
= 65°40' + 2°29' = 68°9'. Cutting angle of gear = 65°40' - 2°53' 
= 62°47'. 

Outside Diameter of the Blank. The preceding data give the 
various angles of the blank, but it remains to compute the outside 
diameter 0. This is derived from data already known, by following 
this rule: 

Multiply the cosine of the pitch angle by twice the addendum 
and add to the pitch diameter, that is, 

= D + 2S x Cosoo . Fig. 289 

Selecting the Cutter. The best results are obtained if we select 
a cutter, not for the number of teeth that the gear is to have, but 
the proper cutter for an imaginary spur gear with an entirely differ- 
ent diameter, and consequently, with an entirely different number 
of teeth. The radius of our gear is AC, but the radius of the imagi- 
nary gear for which we select our cutter is AE. Similarly, the radius 
of the imaginary gear for the pinion is AD. If we know the length 
of the radius AE, then AE x 2 = diameter; diameter x 5 = number 
of teeth of the imaginary gear. 

To find AE: 

In triangle AOE, AO and angle AOE are known. 



310 The Cincinnati Milling Machine Company 

AF 
Tan AOE = — , therefore AE = tan AOE x AO. 
AO 

AOE = 65°40' and its tangent is 2.21132. 
AO = 4.61111. 

Therefore, the radius AE = 2.21132 x 4.61111 = 10.1966. 

The diameter = 20.393 and the number of teeth 
is 5 x 20.393 = 101.96, or 102 teeth. 

In a similar manner we find the length of the line DA, by multi- 
plying the length of OA by the tangent of angle DOA, and find that 
AD equals 2.0852; the diameter of the imaginary gear for the 
pinion would be twice that much, or 4.1704, so that the number of 
teeth of this imaginary gear would be 20.85. We would therefore 
select a cutter suitable for 21 teeth and not for 19 teeth. 

The preceding paragraphs will serve to show how simple and 
practical a tool trigonometry really is in solving ordinary shop 
problems, and also, the method followed in computing bevel gears. 
Practical rules and formulas for quick reference are given at the end 
of this chapter. 

Cutting Bevel Gears. We are concerned here with cutting 
bevel gears with a rotary cutter on a Milling Machine. Such gears 
are of course not entirely correct in their tooth forms. This is not 
the fault of the milling machine but is due to the fact that the size 
and shape of a bevel gear tooth is different at every point through- 
out its length while the section through the tooth of a gear cutter 
can have only one size and shape. Such a cutter may be correct 
for any one section of the bevel gear tooth but can not possibly be 
correct for all, or even two of them. 

While such gears may not be good enough for refined machinery, 
they are, in a great many cases satisfactory for all ordinary pur- 
poses. 

The following will show how such gears may be cut as nearly 
correct as is practical with a rotary cutter on a milling machine. 

The Shape of the Tooth. Fig. 283 shows a tooth of a Bevel 
Gear. The large outline is the shape of the tooth at the outer end 
of the gear, say Q (Fig. 282), and the smaller outline is the shape of 
the tooth at the inner end, R. When cutting a bevel gear on a 
milling machine, the dividing head is set in accordance with the 



A Treatise on Milling and Milling Machines 311 

computed cutting angle for the gear, in other words so that the 
bottom of the tooth is horizontal. The line representing the bottom 
of the tooth passes through the apex of the cone and the cutter 
forms the outline APB, Fig. 283. This outline can be made so as 




Fig. 283 

to be correct for the large end of the tooth. The illustration shows 
at once that it is not correct for the small end of the tooth which 
should follow the outline API^. In order to make the gear more 
nearly correct, we would have to file some off the small end of the 
tooth at the top and fill it up slightly at the bottom. Such filling 
up is, of course, impossible. The filing off is quite commonly done 
with bevel gears made with a rotary cutter. The distance AA X is a 
measure of the amount we have to file off the top of the tooth. 
If we had selected a cutter that was not quite correct for the large 
end, nor for the small end, but for a point half way between, we would 
have had less to take off the top of the teeth, but the undercut at 
the bottom of the teeth would have been somewhat more pro- 
nounced. Ordinarily a cutter is selected which makes the correct 
shape at the large end of the teeth — and that for two main reasons. 
In the first place we can watch the action of two mating teeth at 
the large end, but at no other section. In the second place, the 
pressure at the large end causes the least wear and deformation of 
the teeth. Therefore, bevel gears are designed to have the pressure 
concentrated at that large end. 

We have shown in a preceding paragraph how to select the cutter 
for a given pair of bevel gears. We found, for instance, that the 
large gear in Fig. 282 should be cut with a cutter that will cut a 
spur gear of 102 teeth. If the circular pitch of a bevel gear is 1", 
then the thickness of the tooth on the pitch line at the large end is 
Y", and therefore, the width of the space is also }/%'. The cutter 
that would cut this space would be Y^' thick at the pitch line. If 



312 



The Cincinnati Milling Machine Company 



this cutter were of a rectangular shape, as at A, Fig. 284, then it 

would cut a space through the bevel gear of even width throughout. 

In other words, the space at the small end of the tooth would be 

exactly the same width as at the large end. Of course this would 






Fig. 284 

not do, as this space must be proportionately smaller at the small 
end. In order to use a cutter of such a shape we must select one 
thin enough to pass through the tooth space at the small end. If 
the cutter were of the shape shown at B, Fig. 284, then it would 
automatically make a space of the proper width at any section of 
the tooth, and the flanks of all the teeth would converge properly 
toward the apex. Such a cutter might be used, for instance, for 
cutting saw-tooth clutches, and the bevel sides of these saw-tooth 
clutches would bear over their entire length. A cutter of the general 
shape as shown at C, Fig. 284, has some of the peculiarities of the 
square tooth A, and of the triangular tooth B. Consequently, 
we must select a cutter thinner than the width of the space at the 
large end; in fact, at least as thin as the width of space at the small 
end. 

Tooth Elements. In Fig. 282 OQ is called the cone radius. 
OR is also a cone radius, but whereas OQ is the cone radius for the 
large end, OR is the cone radius for the small end. Thickness of 
tooth, pitch, height of tooth, in fact, all the elements of a tooth 
anywhere in the bevel gear are in direct proportion to the cone 
radii. If, for instance, OQ were twice as great as OR, then the pitch 
at Q would be twice as great as the pitch at R; the height of the 
tooth at Q would be twice as great as the height of the tooth at R, 
etc. If then, we know the pitch of a gear at the large end and the 
cone radii at the large and small ends, we can easily figure the 
pitch at the small end. If, for instance, we select the same elements 
of the gears as we found in Fig. 282, and make the face of the gear 
RQ equal 1", then we find the following: OQ = OA = 4.611". OR = 
OQ - 1" = 3.611. The pitch at Q is 5, or, expressed as circular pitch, 



A Treatise on Milling and Milling Machines 313 

.628", and the pitch at R is found by multiplying this pitch at Q 
by 3.611 and dividing it by 4.611; that is 

Pitch at small end = — x Circ. P. = ^^ x .628 = .492. This 

OA 4.611 

gives for the pitch at R .492 // . We must then select a cutter which 
is not thicker than half this pitch at the height of the pitch line at 
R. Any cutter which is thinner will do, but a cutter which is thicker 
can not be used. In order to determine the correctness of the cutter 
we must measure it at its pitch line FOR the small end. Since all 
the tooth parts at the small end are in exact proportion to the cone 

q C1 1 

radii, that is, diminished — , we first find the thickness at the 

4.611 

pitch line of a cutter that would be correct for the large end only. 
We know that the cutter tooth has a height above the pitch 
line = dedendum + clearance. 

Pitch = 5, therefore dedendum = .2. 

Clearance = — = — = .0314, which added to the deden- 

P 5 

dum .2 gives us the pitch line .2314" down from the top of the 

cutter tooth. For the small end then we have .2314 x — = . 181*. 

4.611 

We have already found that the pitch (circular) at the small 
end is .492, therefore the width of the tooth space at the small 
end is one-half this, or . 246. 

We now measure the cutter by setting a tooth gauge for a depth 
of . 181" and a width of . 246". The cutter must pass through this 
gauge; if not, it is too thick and we must select another cutter. 

The whole depth to be cut in the gear at the large end is, adden- 
dum + dedendum + clearance = .2 + 2 + .0314 = .4314", and at 

the small end .4314 x ^^ = .3379". 

4.611 

We now know the whole depth of tooth spaces at both ends = 
.4314" and .3379". The thickness of the teeth at both ends = 
.314" and .246". The height of the teeth above the pitch line at 
both ends = .200 and .157. The cutting angle = 62°41'. 



314 



The Cincinnati Milling Machine Company 



Setting the Machine. With the proper cutter in place on the 
arbor, we bring the milling machine table into such position that 
the cutter is exactly central with the dividing head spindle. Then 
with the gear blank securely held in place we set the dividing head 
to bring the gear to the proper cutting angle = 62°41'. 

The swivel of the dividing head is graduated to read with the 
spindle horizontal and therefore 90° when vertical. When set 
beyond the vertical position the graduations read in reverse order; 
that is, 80°, 70°, and so on; in other words, the complement of the 
angle beyond the vertical. This is done so that for any position of 
the dividing head spindle, whether ahead of, or past the vertical, 
the graduations will always show the angle which the spindle makes 

with the horizontal position. 
We, therefore, need merely 
swing the dividing head 
spindle past the vertical to 
62°41 / and our gear blank is 
at the correct angle for tak- 
ing the cut. It is shown in 
this position in Fig. 285. 

It should be noted that 
the gear is always set at the 
angle past the vertical as of 
Fig. 285, so the direction in 
the cut will be away from 
instead of toward the divid- 
ing head spindle. One of the 
many advantages of the 
Fig. 285. Bevei Gear Cutting Cincinnati Dividing Head is 

that for such work it can be set past the vertical far enough to 
obtain the cutting angle for all bevel gears up to and including 
mitre gears. 

With this setting made we set for depth of cut by the usual 
method of touching the cutter to the blank at the extreme edge 
of the large end of the tooth; i. e., the point of largest diameter 
of the gear, then raise the table the amount required for the whole 
depth; in the case of the above gear = .431. The exact relation of 
the cutter to the blank is shown in Fig. 286. 

After having made this setting we take a central cut through 
each tooth space. This is not absolutely necessary, but it is recom- 




A Treatise on Milling and Milling Machines 315 



mended here. If we were to attempt to mill the gear by taking only 
two cuts, the first cut would finish at once one side of a tooth, and 
we would then have considerable metal left to be removed when 
taking the final cut, finishing the side of the next tooth. This would 




Fig. 286 

tend to crowd the cutter to one side and would probably cause an 
unevenly cut gear. We therefore recommend taking first a central 
cut and then two finishing cuts, one on each side of the tooth 
space. 

After having taken the first cut all around the gear it will be neces- 
sary to make certain adjustments of the blank in relation to the 
cutter in order to produce a tooth of the proper thickness and as 



316 



The Cincinnati Milling Machine Company 



nearly as possible the correct form. Two things are necessary: 
the rotation of the blank and the offset; that is, setting the cutter 
out of center. We will first determine the amount of offset. 

Computing the Offset. The formula quite generally used is: 

2 P 

in which is the amount of offset. 

T is the thickness of cutter tooth at the pitch line cor- 
responding to the large end of the tooth. 
R is the factor selected from the table. 
P is the pitch of the gear. 

The factor R is taken from the table for set-over. We must 
first find the value I — J which is the ratio between the pitch cone 

radius and the face of tooth. 

TABLE FOR OBTAINING SET-OVER FOR CUTTING BEVEL GEARS 



l_ - 
o «> 


Ratio of Pitch Cone Radius to Width of Face 1 — 1 


2* 


3 


H 


H 


3| 


4 


4* 


4* 


H 


5 


5y 


6 


7 


8 




1 

.254 


l 


l 


l 


1 

.257 


l 


1 


l 

.258 


i 


1 


1 


1 


1 


1 


.254 


.255 


.256 


.257 


.257 


.258 


.259 


.260 


.262 


.264 


2 


.266 


.268 


.271 


.272 


.273 


.274 


.274 


.275 


.277 


.279 


.280 


.283' .284 


3 


.266 


.268 


.271 


.273 


.275 


.278 


.280 


.282 


.283 


.286 


.287 


.2901.292 


4 


.275 


.280 


.285 


.287 


.291 


.293 .296 


.298 


.298 


.302 


.305 


.308 .311 


5 


.280 


.285 


.290 


.293 


.295 


.296 .298 


.300 


.302 


.307 


.309 


.3131.315 


6 


.311 


.318 


.323 


-.328 


.330 


.334 .337 


.340 


.343 


.348 


.352 


.3561.362 


rr 
i 


.289 


.298 


.308 


.316 


.324 


.3291.334 


.338 


.343 


.350 


.360 


.370,. 376 


8 


.275 


.286 


.296 


.309 


.319 


.3311.338 

1 


.344 


.352 


.361 


.368 


.380.386 



NOTE.— For obtaining set-over by above table, use this formula: 

T factor fro-m table 

Set-over = 

2 P 

P = diametral pitch of gear to be cut. 
T — thickness of cutter used,, measured at pitch line 

Now applying this to our gear: We have seen that we should 
use a cutter correct for 102 teeth. This is a No. 2 cutter. We will 
assume it to be . 175 thick at the pitch line. The pitch cone radius 
is the line OC, Fig. 282, which we have found to be 4 . 6" long. The 
face of the tooth is 1". Therefore, 

C_ _ 4^6 

F ~ 1 ' 



A Treatise on Milling and Milling Machines 317 



4 5 

The nearest figure to this in the table is -^-. We will use this. 

1 

4 5 
From the table we find under — and opposite 2, the factor .274. 



We now have these values: 



T = .175". 
R = .274. 
P = 5. 



Substituting, we have 



= — - — = .0875 - .0548 = .0327". 
2 5 

This is the amount the cross slide must be adjusted. 

We now proceed as follows: Set the cutter out of center the 
above amount by adjusting the cross slide, reading the setting from 
the dial. We must rotate the blank in the opposite direction from 
that in which we made the offset. This is shown in Fig. 287. If 

the blank has been offset to the right, it 
must be revolved to the left to bring the 
side of the tooth to be finished towards 
the corresponding side of the cutter again. 
The amount that the blank is revolved 
must be determined by trial, and is cor- 
rect when a trial cut will cover the entire 
surface of this side of the tooth. After 
cutting several teeth on one side it is de- 
sirable to cut the opposite sides of these 
same teeth for trial. To do this, adjust 
the cross slide to bring the blank central 
with the cutter and then continue to adjust 
it the same amount as before, but in the 
opposite direction, and rotate the blank the same amount but 
in the opposite direction. After having milled a tooth with this 
new setting, measure both the large and the small ends at their 
pitch line. If it is found that the large end of the tooth is 
too thick and the small end is correct, the blank was not off- 




Fig. 287 



318 



The Cincinnati Milling Machine Company 



set enough; on the other hand, if the small end is too thick 
and the large end is correct, it was offset too much. Generally 
speaking, if the small end is too thin, it indicates that the offset 
was not enough, and if the small end is too thick, the offset has been 
too much. If the tooth as measured is not correct, then we must 

correct the settings in accordance with the 
above, using slightly more or slightly less 
offset, as the case may be, and revolve the 
blank correspondingly. 

It must be borne in mind, however, 
that exactly the same setting must be made, 
but in the opposite direction for both sides 
of the teeth. When the final setting has 
been determined it is well to make a 
.permanent record of it for future use. 




Fig. 288 



When rotating the blank in accordance with the above, it will 
sometimes happen that when the tooth face is in the correct rela- 
tion to the cutter the index pin will not enter the nearest hole in 
the index plate. We must then loosen the index plate lock and re- 
volve the plate, being careful not to disturb the position of the index 
pin handle until the pin drops into one of the holes, then lock the plate 
in position again. 

After the gear has been cut it will be found that the teeth at 
the small end have their sides too straight; that is, they are too 
thick at the top, and this must finally be corrected by filing a tri- 
angular area from the point of the tooth at the small end down to 
its pitch line and back towards the point of the tooth at the large 
end, Fig. 288. 



A Treatise on Milling and Milling Machines 319 



Formulas for Bevel Gear Calculations 

From the foregoing the following rules and formulas have been 
deduced. These, like the preceding discussion apply to bevel 
gears with shafts at right angles, which of course, include 
mitre gears. The notation used in the formulas, which is easily 
understood by comparing the formula with the corresponding rule, 
is as follows: 



N = 
P = 
'P = 

7T = 
OC = 

T = 
D = 

S = 

s + 
w = 
T = 

C = 
F = 

s = 

t = 



* = 
3 = 

i = 

K = 
O = 
J = 

3 = 
N' = 



number of teeth. 

diametral pitch. 

circular pitch. 

3.1416. 

pitch cone angle and edge 

angle, 
center angle, 
pitch diameter, 
addendum. 

A =dedendum + clearance, 
whole depth of tooth space, 
thickness of tooth at pitch 

line, 
pitch cone radius, 
width of face, 
addendum at small end of 

tooth, 
thickness of tooth at pitch 

line at small end. 
addendum angle, 
(dedendum + clearance) 

angle, 
face angle, 
cutting angle, 
angular addendum, 
outside diameter, 
vertex distance, 
vertex distance at small end. 
number of teeth for which to 
select cutter, also called 
"number of teeth in equiva- 
lent spur gear." 



BnGiJI.HR 
nOOENDUM^K 



WHOLE DEPTH OF TOOTH-W 
RODENOUM tS 




EDGE BNGlE = a. 



FRCE HNGLE 



OEDENOUM f CLEARANCE 
ANGLE =f 
ADDENDUM HNGLE =6 



Fig. 289 



320 



The Cincinnati Milling Machine Company 



Rules and Formulas for Calculating Bevel Gears with 
Shafts at Right Angles 

ocp = Pitch cone 
angle of 
pinion; 

ocg = Pitch cone 
angle of 
gear; ^\ 

Np = Number of ~j—*- — ■ 
teeth in 
pinion, 
etc. 





Fig. 290 



Fig. 291 



Use Rules and Formulas Nos. 1 to 21 in the order given 



No. 


To Find 


Rule 


Formula 


1 


Pitch Cone 
Angle (or 
Edge Angle) 
of Pinion 


Divide the number of teeth in the 
pinion by the number of teeth in the 
gear to get the tangent 


Np 

tan <x p = 

No 








2 


Pitch Cone An- 
gle (or Edge 
Angle) of Gear 


Divide the number of teeth in the 
gear by the number of teeth in the 
pinion to get the tangent 


No 
tan oc o = 

Np 








3 


Proof of Calcu- 
lations for 
Pitch Cone 
Angles 


The sum of the pitch cone angles of 
the pinion and gear equals 90° .... 


ap + ag = 90° 


4 


Pitch 
Diameter 


Divide the number of teeth by the 
diametral pitch; or multiply the 
number of teeth by the circular 
pitch and divide by 3 . 1416 


N NP' 

D = — = 

P X 


5 


a 

o 

'3 
'3. 
~o 
a 

c3 
u 

c3 
<D 
bi 

ja 
-*j 
o 

£i 
i* 
o 

s 

C3 
on 

© 

Xi 

+3 

05 
U 

c3 

TO 

a 
# o 

'to 

a 
<o 

J 

TO 

o> 
H 


Addendum 

Dedendum + 

clearance 
S+A 


Divide 1 by the diametral pitch; or 
multiply the circular pitch by 0.318. 


1 

S = 

P 
= 0.318 P' 


6 


Divide 1.157 by the diametral pitch; 
or multiply the circular pitch by 
0.368 


1.157 

S+A = 

P 
= 0.368 P' 


7 


Whole Depth 
of Tooth 
Space 


Divide 2.157 by the diametral pitch; 
or multiply the circular pitch by 
0.687 


2.157 

W = 

P 
= 0.687 P' 


8 


Thickness of 
Tooth at 
Pitch Line 


Divide 1.571 by the diametral pitch; 
or divide the circular pitch by 2 ... . 


1.571 P' 
P 2 


9 


Pitch Cone 
Radius 


D 

Multiply the radius — by the cose- 

2 
cant of the pitch cone angle 


D 

C=CosecDx — 
2 



A Treatise on Milling and Milling Machines 321 



Rules and Formulas for Calculating Bevel Gears with Shafts 
at Right Angles — Continued 



No. 



10 



To Find 



g |Addendum 
J of Small 
- End of 
Tooth 



Rule 



Subtract the width of face from the 
pitch cone radius, divide the re- 
mainder by the pitch cone radius and 
multiply by the addendum 



Formula 



C-F 

s = S X 

c 



11 



Thickness of 
Tooth at 
Pitch Line at 
Small End 



Subtract the width of face from the 
pitch cone radius, divide the remain- 
der by the pitch cone radius and 
multiply by the thickness of the 
tooth at the pitch line 



C-F 

t = T X 



12 



Addendum 
Angle 



Divide the pitch cone radius by the 
addendum to get the cotangent. . . 



Cotan = 



S 



13 



Dedendum 
+ Clearance 
Angle 



Divide the pitch cone radius by the 
dedendum-f- clearance (S + A) to get 
the cotangent 



Cotan = 



C 



S + A 



14 Face Angle 



Subtract the sum of the pitch cone and 
addendum angles from 90° 



3=9O°-(oc+0) 



15 Cutting Angle 



16 



Angular 
Addendum 



Subtract the dedendum angle from 
the pitch cone angle 



C = « - * 



Multiply the addendum by the cosine 
of the pitch cone angle 



K=SX cos a 



Outside 
Diameter 



18 



19 



Add twice the angular addendum to 
the pitch diameter 



= D +2X 



Apex Distance 



Apex Distance 
at Small End 
of Tooth 



Multiply one-half the outside diame- 
ter by the tangent of the face angle 



O 
J= — Xtan 8 
2 



Subtract the width of face from the 
pitch cone radius; divide the re- 
mainder by the pitch cone radius and 
multiply by the apex distance 



C-F 

j=JX 

C 



20 



21 



Number of 
Teeth for 
which to 
Select Cutter 

Proof of Calcu- 
lations by 
Rules Nos. 9, 
12, 14, 16 
and 17 



Divide the number of teeth by the 
cosine of the pitch cone angle 



N 

N' = 

cos 



The outside diameter equals twice 
the pitch cone radius multiplied by 
the cosine of the face angle and 
divided by the cosine of the adden- 
dum angle 



= 



2 CXcos S 



cos 



322 



The Cincinnati Milling Machine Company 



Rules and Formulas for Calculating Miter Bevel Gearing 





Fig. 292 



Fig. 293 



Use Rules and Formulas Nos. 22, 4-8, 23, 10-13, 24-26, 17-19, 27 and 21 in 
the order given. All dimensions thus obtained are the same for both gears of a 
pair. 



No. 



To Find 



Rule 



Formula 



22 


Pitch Cone 
Angle 


Pitch cone angle equals 45° i 


oc 


= 45° 


23 


Pitch Cone 
Radius 


Multiply the pitch diameter by . 707. 


c 


= 0.707 D 


24 


Face Angle 


Subtract the addendum angle from 
45° 


8 = 


= 45° - 6 


25 


Cutting Angle 


Subtract the (dedendum -f clearance) 
angle from 45° 


£ : 


= 45° - $ 








26 


Angular 
Addendum 


Multiply the addendum by . 707 ... 


K 


= 0.707 S 



27 



Number of 
Teeth for 
which to 
Select Cutter 



Multiply the number of teeth by 1.41. N' = 1 . 41 A 7 



A Treatise on Milling and Milling Machines 323 



CHAPTER XVI 

SPIRAL GEAR CUTTING 

Spiral gears may have their axes parallel, the same as spur 
gears, or the axes may be at an angle with each other. A spiral 
gear differs from a spur gear in that the teeth are not placed parallel 
with the axis, but are wound spirally around the pitch circle. The 
name "spiral gears' ' is really wrong. The teeth are not wound in a 
spiral, but in a helix around the pitch circle. The distinction 
between a spiral and a helix will be clear when we remember that the 
main spring of a watch is a good example of a spiral, while the 
threads on a lead screw form a helix. However, in our discussion, 
we will use the name "spiral gears," as this is the name by which 
the average mechanic knows them. This chapter will not treat 
of all the properties of spiral gears, but only of such as need be known 
in order to design or make them. 

If we have two shafts with a center distance of 7J4"> an d we 
must drive one shaft from the other with a given speed ratio, we 
will find considerable trouble if we try to use spur gears. If, for 
instance, the speed ratio is 4 to 5, we will not be able to use spur 
gears except by making them 18 pitch. The sum of the diameters 
is 14 J^", being twice the center distance, and we must select the 
pitch so that the sum of the numbers of teeth of the two gears can 
be split up into two numbers which have a ratio of 4 and 5. If we 
should select 4 pitch for the gears, we would find that the sum of the 
numbers of teeth of these two gears is 4 times the sum of their diame- 
ters, or 4 times 14 3^ equals 58. However, 58 can not be split up 
into two numbers which have a ratio of 4 and 5. In order to do so, 
58 should be divisible by 4 plus 5 which equals 9. If we should 
select 5-pitch gears, then the sum of the numbers of teeth of the 
two gears would be 5 x 14J^ = 723^2, and this, of course, is impossi- 
ble, as the sum of the number of teeth of two gears must be an 
integral number. If we make the pitch 18, then the sum of the 
numbers of teeth of the two gears would be 18 x 143^ = 261, and 



324 The Cincinnati Milling Machine Company 

4 5 

one gear would have — of 261 teeth, and the other gear — of this num- 

«/ y 

ber. However, 18 pitch is probably entirely too fine for the work 
we have to do, so that we must choose one of two things. We must 
either make special cutters with an odd pitch, or we must be satis- 
fied with a compromise as to the gear ratio. The first of these two 
things is costly and consumes a great deal of time and the other 
may be absolutely prohibitive if an exact gear ratio is required. 

Substituting spiral gears for spur gears would solve the question 
at once. 

Definitions — Pitch, Lead, Normal Pitch, etc. A tooth of a 
spiral gear is much like the thread of a screw. It does not have the 
same cross section, nor is it meant to do the same kind of work, but 
in many respects the two are very similar. The distance from a 
point on a screw thread to the corresponding point on the next 
thread is called the pitch. The distance the screw travels in an 
axial direction, if we give it one complete turn, is called the lead. 
These same terms apply in the same way to a spiral gear. There is, 
however, this distinction: We measure the pitch of a screw along the 
axis of the screw, whereas, we measure the pitch of a spiral gear around 
the circumference, that is, at right angles to the axis. However, 
there are two things which are called pitch in the spiral gear. The 
pitch, as we described it, that is, the distance between two cor- 
responding points of two adjoining teeth measured at right angles 
to the axis, is called the real pitch, whereas the distance between 
two corresponding points of two adjoining teeth, measured in a 
direction at right angles to the direction of the teeth, is 
called the normal pitch. The normal section, which would give 
us the normal pitch, would show us the true section of the teeth. 
A section, taken at right angles to the axis, would give us the dis- 
torted view of the shape of the teeth as seen when looking at the 
end of a spiral gear. A section through the axis would also give a 
distorted view. If the spiral angle is 45°, then the distorted views of 
the teeth would be the same whether we take the sections through 
the axis, or at right angles with the axis. If the angle of the spiral 
with the axis is less than 45°, that is, if the spiral gear approaches 
more nearly a spur gear, then the right angle section would give a 
less and the axial section a more distorted view. This is reversed 
if the angle of the spiral with the axis is more than 45°, that is, if 
the spiral gear approaches more nearly the shape of a worm. 



A Treatise on Milling and Milling Machines 325 

Cutting Spiral Gears. Spiral gears are ordinarily cut with 
common spur gear cutters. The normal pitch is, therefore, given 
in the same way as the pitch of spur gears, that is, we talk of a 5, 
a 7, or a 10-pitch gear. The real pitch is measured along the cir- 
cular section of the gear, and if this pitch is P' and the number of 
teeth of the gear is n, then the length of the circumference of the 
circular section is nP'. 




BB = RXlS 
T - TOOTH LINE 
P,= NORMRL PITCH 
P'= RERL PITCH 
L e SPIRRL RNGLE 
n * NUM6ER OF TEETH 

Fig. 294 



Fig. 294 shows that the normal pitch and real pitch bear such 
a relation to each other that the normal pitch is a right angle side 
of a right angle triangle, of which the real pitch is the hypotenuse 
and the tooth line is the base. If the angle between the tooth line 
and the axis is called L, and if the normal pitch is P, then the real 
pitch P', is P-secant-L. If we know the pitch of the cutter, the number 
of teeth and the spiral angle, we can easily figure the pitch diameter 
of the spiral gear. We figure as if it were a spur gear and then multi- 
ply the diameter by the secant of the spiral angle. For instance, a 



326 



The Cincinnati Milling Machine Company 



spiral gear with 16 teeth, 5 pitch, and a spiral angle of 37 degrees, 
will have a diameter of 16 divided by 5 and multiplied by the secant 
of 37 degrees. If we were dealing with a spur gear the pitch diameter 

would be — = 3.2". 
5 

From a table of secants we find sec 37° = 1.2521. Then we 
have 3.2 x 1.2521 = 4.0067", the pitch diameter of the spiral gear. 

The pitch circumference is 4.0067 x x = 4.0067 x 3.14159 = 
12.587". 

If we should make a wooden cylinder with a diameter equal to the 
pitch diameter of out' spiral gear, and then cut out a paper right 
angle triangle, Fig. 295, of which one right angle side is equal to 
the circumference of the pitch circle, and the opposing angle equal 









AXIS OR CENTRE LINE OP^ 


S£EAR 








l_ ^s^ 


LERO 




/SPlRHL 3nGlE^ s s. 



Fig. 295 

to the spiral angle, and wrap this triangle around the cylinder, 
we will find that the hypotenuse describes a spiral line around the 
cylinder, and that the end of the hypotenuse will come in line with 
the beginning. In other words, the two ends of the hypotenuse 
will be a distance apart on the cylinder equal to the lead of the 
spiral. If now we unwrap the paper triangle we have in this triangle 
all the important elements of a tooth of the spiral gear. One right 
angle side is the circumference of the pitch circle, the second right 
angle side is the lead, the hypotenuse is the length of a tooth 
wrapped once around the pitch cylinder, the angle opposite the 
circumference is the angle of the spiral with the axis of the gear. 
This is commonly called the spiral angle or helix angle. It is the 
angle to which the milling machine table must be set. The angle 
opposite the lead is the angle which the tooth makes with the body 
of the gear. 



A Treatise on Milling and Milling Machines 327 

Addendum, dedendum and clearance are the same as in a spur 
gear of the same pitch as the normal pitch of the spiral gear. 

Selecting the Cutter. It is now possible to figure all the 
dimensions of the spiral gear and turn up the blank in the lathe. 
However, when it comes to cutting the teeth, a new element comes 
in. Although the gear may have 16 teeth, 5 pitch, this does not 
mean that we can use a 16-tooth, 5-pitch gear cutter for this spiral 
gear. It is true, we will have to use a 5-pitch cutter, but not for 
16 teeth. We must select a spur gear cutter for a different number 
of teeth. The rule usually given is to divide the number of teeth 
of the spiral gear by the cube of the cosine of the spiral angle. 

This gives good results for gears having a spiral angle in the 
neighborhood of 45°, but anyone who has followed this rule for 
gears with a spiral angle differing greatly from 45° will have found 
that such gears do not run properly and the running of the gears 
becomes worse as the spiral differs more from 45°. For such gears 
we recommend the following rule: 

Divide the number of teeth of the spiral gear by the product of the 
square of the cosine multiplied by the sine of the spiral angle. 

N = in which N is the number of teeth of the 

Cos L 2 x sin L 

selected gear cutter, and n is the number of teeth of the spiral gear. 
Taking the above case 

N = - -i 1 - • 16 - ** = 41. 

Cos 37 2 x sin 37 .79864 2 x .60182 .6378 x .60182 

We should select a cutter suitable for cutting a gear with 41 teeth. 

The speed ratio of two spiral gears is, as with spur gears, the 
ratio of their numbers of teeth. For instance, a 16-tooth gear 
driving a 32-tooth gear will cause this latter gear to run half as 
many revolutions per minute as the former. The center distance 
between two spiral gears, as with spur gears, is equal to half the 
sum of their pitch diameters. 

Shafts Parallel. Computation of a pair of spiral gears which 
are to be used in place of spur gears. 

If we have two shafts, say 8" apart, and wish to drive one from 
the other by means of spiral gears with a given gear ratio, and, if 
we desire to use standard gear cutters we should proceed as is shown 
in the following example : 



328 



The Cincinnati Milling Machine Company 



The two gears shown in Fig. 296 must have a ratio of 2 to 1; 
a center distance of 8", and in order to make them of the proper 
strength the teeth must have about 5 pitch. As we want to use 
standard gear cutters, we will make the pitch exactly 5. 




SMftLl GERR 
NUMBER OFTEETH=n-25 
SPiRBL RNGLE-20°2l' 
RiGmt hrnD 



LRRGE GERR 
NUMBER OP TEETH = 2nr50 
SPIRHL RNGuE = 20 e 2l' 
LEFT HRND 



Fig. 296 

A pair of spiral gears on parallel shafts to give a speed ratio of 2 to 1. 

Number of Teeth and Spiral Angle. Taking the number 
of teeth in the small gear = n, and the number in the large gear = 
2n, and the spiral angle of the teeth in the small gear L, we have: 

Pitch diameter small gear = , and 



Pitch diameter large gear = 



5 

2n sec L 



, because, in a pair of spiral 



gears with shafts parallel, the spiral angle is the same in both. 
The sum of the pitch diameters of the gears is, therefore, 

n sec L 2n sec L 
and this sum equals double the center distance. 



A Treatise on Milling and Milling Machines 329 

Therefore, 

— sec L h sec L = 16. (double the assumed center 

5 5 

distance.) 

Multiplying both sides of this equation by 5, in order to simplify 
it, we get 

n sec L + 2n sec L = 80. 

This is a very simple equation, but unfortunately there are two 
unknown quantities: The number of teeth n, and the spiral angle 
L. However, there is one thing we know about n; it must be an 
integral number. There is still another thing we know, and that is 
that we would like the angle to be about 20 degrees, for this gives 
the maximum efficiency of the gear system. We will, therefore, 
try the equation by giving L the value of 20° : sec 20 = 1 . 0642, and 
therefore the equation 

n sec L + 2n sec L = 80 

becomes (n x 1.0642) + (2n x 1.0642) = 80. 

3n x 1.0642 = 80. 
n x 3.1926 = 80. 

n = 25.058. 
2n = 50.116. 

As n must be an integral number, we will assume a value of n = 25, 
and therefore 2n = 50. 

Substituting in the above equation, we get 

25 x 1.0642 + 50 x 1.0642 = 79.815. 

Since the second member of the equation should be 80 and not 
79 . 815, it is evident that the assumed value of 20° for L, the spiral 
angle will not do, if we decide to use 25 and 50 teeth. In proceeding 
to find the correct angle, we will first determine whether the angle 
should be more or less than 20°. For trial, we will select 19° and 21°. 
With 20° the value of the second member was too small. Therefore, 
it must be increased. Since our value is too small we will try a 
larger angle, 21°: 

sec 21 = 1.0711. Substituting this in our equation, we get 
25 x 1.0711 + 50 x 1.0711 = 80.3325. 



330 The Cincinnati Milling Machine Company 

The value, using 20°, was .185 too small. Our new value is .3325 
too large. The correct angle is. therefore, between 20° and 21 : . 
By trial, we find that 20 : 22' sec 20 : 22' = 1 . 0667 gives us 

25 ■ 1 0667 - 50 ■: 1.0667 = 50.0025. or .0025 too large. 
and 20 : 21' sec 20 : 21' = 1.066 gives us 

25 ■ 1.066*3 - 50 ■: 1.0666 = 79.9950. or .005 t00 sma n. 

We will, therefore, choose as our value 0: L. 20 : 21'. Let us try 
this out and find what the new center distance between the gears 
will be. 

Since the gears are 5 pitch and we have taken 2 x center distance 
for our second member of the equation, then the center distance is 

79 9 C ^50 
- • - - — 1 _ - 99951) 

2x5 

which is .0005'" short, which is close enough for all practical pur- 
poses." Our gears, therefore, will have a spiral angle of 20 = 21'. 
the small one with 25 teeth and the large one with 50 teeth. 

Selecting the Cutter. Referring back to the rule given on 

page 327. we have for the small gear 

x = n 25 

cos : 20=21' x sin 2o : 21 .93759- ■ .34775 

25 

— = £l- 

.s.NJ x .34775 

and for the large gear 

50 50 

= = loo. 

. 93759- x .347,5 .8780 x .34775 

Therefore, the cutters should be selected for SI and 163 teeth 



* We have already decided that the center distance between the shafts 
on which these gears will work in our machine is 3 r . "Were we to use an angle 
::' 20 : 22 . : .:: rears TouLi have a :e:::e: i:s:ar.:-= '. ••'. J23' ::: large, ar.i :hey 
would not go into place, or at least they would work too tight if all other dimen- 
sions were correct. We therefore choose 20° 21' which makes gears that are 
.0005" small and will have just this much working clearance. This is satisfac- 
tory for ordinary work. If closer accuracy is required we must either change 
our center distance in the machine or continue trying by selecting angles read- 
ing in seconds until a satisfactory one is found. 



A Treatise on Milling and Milling Machines 331 

Computing the Lead. Referring to Fig. 295: We know 
angle L = 20°21'. However, we do not know the pitch circum- 
ference. We must therefore first find the 

PITCH DIAMETERS 

Pitch diameter = — x sec L. 
P 

Then for the small gear we have 

— x sec 20°21' = — x 1.0666 = 5.3330, 
5 5 

and for the large gear 

— x sec 20°21' = — x 1.0666 = 10.666 
5 5 

Since the outside diameter equals the pitch diameter plus twice 

2 

the addendum, OD = PD -\ therefore, 

P 

2 

outside diameter of small gear = 5.3330 -\ = 5.7330"; 

5 

2 

outside diameter of large gear = 10 . 6660 -{ = 11 . 0660". 

5 

The pitch circumferences are: 

small gear 5.333 x 3.1416 = 16.754 
large gear 10.666 x 3.1416 = 33.508. 

T , pitch circumference 16.754 16.754 , firr// 
Lead = - = = = 45. 17" 

Tangent L Tangent 20°21' .37090 

for the small gear, and 2 x 45.17" = 90.34" for the large gear. 

We now proceed to select the change gears by following the 
instructions given in the chapter on Change Gears for Cutting 
Spirals. 

Our gears are as follows, shafts parallel: 

Pitch = 5. 

Number of teeth in small gear = 25. 

Number of teeth in large gear = 50. 



332 The Cincinnati Milling Machine Company 

Spiral angle small gear = 20°21' right hand. 

Spiral angle large gear = 20°21' left hand. 

Pitch diameter small gear = 5 .3330". 

Pitch diameter large gear = 10.6660*. 

Outside diameter small gear = 5 . 7330". 

Outside diameter large gear = 11 . 0660". 

Lead small gear = 45. 17". 

Lead large gear = 90 . 34". 

Cutter for small gear = for 81 teeth. 

Cutter for large gear = for 163 teeth. 

Center distance (exact) = 7 .99950". 

Center distance (actual used) = 8.00". 

The above example is not at all unusual, since spiral gears are 
coming more into general use for transmission members on parallel 
shafts in place of spur gears. 

Shafts at Right Angles. We will now consider the case of a 
pair of spiral gears on shafts that are at right angles with each other, 
Fig. 297, using the same general data as above. 

Speed ratio = 2 to 1. 

Pitch = 5. 

Center distance = 8. 

Spiral angle of small gear = L. 

Spiral angle of large gear = 90° — L. 

or = complement of L. 

Number of teeth in small gear = n. 

Number of teeth in large gear = 2n. 

There is an important point of difference between this and the 
previous case. 

With shafts parallel, we prefer a spiral angle of about 20° to 
reduce the end pressure on the shafts. With shafts at right angles, 
we prefer a spiral angle of as near 45° as we can make it, for this 
gives the maximum efficiency of such a gear system. 

Number of Teeth and Spiral Angle. Since the spiral angle 
of the large gear is the complement of L, we must use the cosecant 
in finding its number of teeth. Our equation then is 



A Treatise on Milling and Milling Machines 333 



RIGHT HRND 
SPIRAL 




L = 46°30' Right Hhnd 

Rngle Op LrrgeGebr 
O0-LJL = 43*30'RtHbm0 



RXIS OF 
LRRGE GE&R 



Fig. 297 

Spiral gears with shafts at right angles 



n sec L . 2n cosec L . n 
+ = 16, or 



n sec L + 2n cosec L = 80. 
sec 45° =1.4142 
cosec 45° = 1.4142 



and therefore, the equation 

n sec L + 2n cosec L 
becomes 



80 



n x 1.4142 + 2n x 1.4142 = 80. 

3n x 1.4142 = 80. 

n x 4.2426 = 80. 

n = 18.85. 

Since n must be an integral number, we will assume n to have 
a value of 19, and therefore 2n equals 38. Substituting these values 
in our equation, we get 

19 x 1.4142 + 38 x 1.4142 = 80.6094. 



334 The Cincinnati Milling Machine Company 

Since the second member of the equation should be 80, it is evi- 
dent that our assumed value of 45° for L, the spiral angle, is incor- 
rect for 19 and 38 teeth. In proceeding to find the correct angle, we 
will first determine whether the angle should be more or less than 
45°. For trial, we select 44° and 46°. With 45°, the value of the second 
member was too large. Therefore, it must be reduced. If we find 
that 44° gives a smaller value than 45°, then we know that the 
angle should be less than 45°, but if the value is greater, then we 
know that the angle must be more than 45°. Of course, we don't 
expect that either 44° or 46° will be the correct value of the angle, 
but making a trial with both will show us in the first place, in which 
direction we must go, and in the second place, how much a change 
of one degree affects the result. 

Assuming an angle of 44°: 

sec 44 = 1.3902 
cosec44 = 1.4395 

we then have 

19 x 1.3902 -}- 38 x 1.4395 = 81.1148. 

This is more than the value resulting from 45°. Therefore, we 
must select an angle greater than 45°. Assuming an angle of 46°: 

sec 46 = 1.4395 
cosec46 = 1.3902 

we then have 

19 x 1.4395 + 38 x 1.3902 = 80.1781. 

This is closer to 80 than we found when L was assumed at 45°, 
but it is still too large. We will, therefore, try an angle of 47°. 

sec 47 = 1.4663 
cosec47 = 1.3673 

we then have 

19 x 1.4663 + 38 x 1.3673 = 79.8171. 

This is too small, whereas the value L = 46 was too large, there- 
fore, the true value of L must be somewhere between 46° and 47°. 



A Treatise on Milling and Milling Machines 335 

We note further that the value for L = 46 is . 1781 too large and for 
L = 47 is . 1829 too small, so that we may expect the true value of 
L to be very close to 46°30'. We will try this, assuming L - 46°30\ 

sec 46°30' = 1.4527 
cosec46°30' - 1.3786 
then 

19 x 1.4527 + 38 x 1.3786 = 79.9881. 

This value is so close to 80, that it is worth while to try it out and 
see what the center distance of these gears will be. 

In our first equation we made the second member 

2 x center distance x the pitch = 2 x center distance x 5 = 80. 

Therefore, the center distance of our new gear will be, 

79 9881 
center distance = — : = 7.99881. 

2x5 

This differs from 8" only a little more than .001", which is close 
enough for all ordinary requirements. However, we do not need to 
stop here if extraordinary accuracy is required. In that case we 
would note that the value of the second member is too small and 
that, therefore, the angle is too large. We would, therefore, try 46° 
20 ' or 46°25' and gradually narrow down until the error is inside 
of the permissible limits. 

By following the same methods as in the previous example, 
we find other needed data as follows: 

Selecting the cutter for the small gear we have 

^r n 19 -- 

" cos 2 46°30' x sin 46°30' .3437 " 

and for the large gear 

N = - - J*- = 105, 

cos 2 43°30' x sin 43°30' .3622 

therefore the cutters should be selected for 55 and 105 teeth respect- 
ively. 

Computing the Lead. Pitch diameter = — x sec L. There- 



336 The Cincinnati Milling Machine Company 



fore, we have for the small gear 

19 19 

— x sec 46°30' = — x 1.4527 = 5.52026, 
5 5 

and for the large gear 

qo qo 

— x sec43°30' = — x 1.3786 = 10.47736. 
5 5 

2 

Outside diameter small gear = 5.520 ^ = 5.920' / . 

5 

2 

Outside diameter large gear = 10.477 -) = 10. 877''. 

5 

The pitch circumferences therefore, are 

small gear 5.520x3.1416 = 17.341 
large gear 10.477 x 3.1416 = 32.914 

T , Pitch circumference 
Lead = 

Tangent L 
We have for the small gear 

Lead = 17841 -J™*L- 16.465- 
Tan 46°30' 1.05378 

and for the large gear 

T , 32.914 32.914 QA aQA „ 
Lead = , = = 34.684". 

Tan 43°30' .94896 

We can now proceed to select the change gears as described in 
the chapter on Change Gears for Cutting Spirals. 

Our gears are as follows — shafts at right angles: 

Pitch = 5. 

Number of teeth in small gear = 19. 

Number of teeth in large gear = 38. 

Spiral angle of small gear = 46°30 / right hand. 

Spiral angle of large gear = 43°30' right hand. 

Pitch diameter of small gear = 5 . 520". 



A Treatise on Milling and Milling Machines 337 

Pitch diameter of large gear = 10.477". 

Outside diameter of small gear = 5.920". 

Outside diameter of large gear = 10.877". 

Lead of small gear = 16 .465". 

Lead of large gear = 34 . 684". 

Cutter for small gear = for 55 teeth. 

Cutter for large gear = for 105 teeth. 

Center distance (exact) = 7.99881". 

Center distance (actual used) = 8. 00". 

Shafts at an Angle of Less than Ninety Degrees. We will 
now consider the case of a pair of spiral gears on shafts at an angle 
of 60° with each other, Fig. 298, using again the same general data 
as in the two previous cases. 

Speed ratio = 2 to 1. 

Pitch of cutter = 5. 

Center distance = 8. 

Spiral angle of small gear = L. 

Spiral angle of large gear = 60° — L. 

Number of teeth in small gear = n. 

Number of teeth in large gear = 2 x n. 



RIGHT HAND 
SPIRAL 



RIGHT HAND 
SPIRRL 




5pmfM.Rfi6i.E0F5rifUi 

GfflR L»2l°l7'RTHqrio. 

5PIRRL RtiGLt Of 
LRR6E GtAR. 

(eo*-L)= , 

L,= 38-43 



Fig. 298 

Spiral gears with shafts at an angle of less than 90 degreee. 



338 The Cincinnati Milling Machine Company 

(a) If the spiral angle of each gear is less than the angle between 
the shafts, then the sum of the spiral angles of the gears will equal 
the shaft angle and the gears will be of the same hand spiral. 

(b) If the spiral angle of one of the gears is greater than the 
shaft angle, then the difference between the spiral angles equals 
the shaft angle and the gears will be of opposite hand spirals. 

Number of Teeth and Spiral Angle. Our equation is again 

n x Sec L 2n x Sec ^60 r -L^ , , 
-I : = 16, or 

5 5 

n x Sec L + 2n x Sec (60°-L) = 80. 

We now have to find the angle L by trial. Let us assume 
L = 20°, then 

n x 1.0642 4- 2n x 1.3054 = 80, or 
1.0642n + 2.6108n = 80 

3.675n = 80 

n = -^- = 21.8 teeth. 
3.675 

Suppose we select n = 22 and find the spiral angle L by assum- 
ing L = 20°, then 

22 x Sec 20° + 2 x 22 x Sec (60°-20°) = 80, or 

22 x 1.0642 + 44 x 1.3054 = 80 

23.414 - 57.437 = 80.850, which is too large. 

Suppose L = 21°, then 

22 x Sec 21° + 44 x Sec 39° = 80 
23.5022 + 56.6148 = 80.117, 

which is still a trifle too large. After trying a few more examples, 
with angles ranging from 21° to 22°, we find L = 21 : 17\ which gives 

22 x Sec 21°17' + 44 Sec 38°43' = 80 

23.6104 + 56.3904 = 80.0008, which is close enough for all 
practical purposes. 



A Treatise on Milling and Milling Machines 339 



Diameters, Circumferences, etc. Then, 

Pitch dia. of small gear = = 4. 722". 



Pitch dia. of large gear = = 11.278". 

5 

Center distance - 3^ (4.722 + 11.278) = 8.000/ 

Outside dia. of small gear = 4.722 + — = 5.122". 

5 

Outside dia. of large gear = 11.278 + — = 11.678". 

5 

The pitch circumferences are: 

Small gear = 4.722 x 3.1416 = 14.834" 
Large gear = 11.278 x 3.1416 = 35.430" 

and the exact leads are for the 

14 834 

Small gear = 38.081" 

Tan 21°17' 

Large gear ' = 44 . 198" 

Tan 38°43' 

Selecting the size of cutter, we have for 

22 

Small gear, N = — = 27.2 teeth 

Cos 2 21°17' x Sine 2117' 

44 

Large gear, N = = 115 . 6 teeth. 

Cos 2 38°43' x Sine 38°43' 

From the table of leads (page 376) we find the closest lead 
for the small gear is 38.182 and the large gear 43.977, and the 
corresponding change gears, 72, 24, 56, 44 and 86, 44, 72, 32. 

This example indicates the procedure for computing a pair of 
spiral gears with shafts at any other angle. 



340 



The Cincinnati Milling Machine Company 



It is important that drawings should be complete with all data 
needed by the shop before they leave the Engineering Department. 
For example: The data that the drawing for the above spiral gears 
should contain are as follows: 



Pitch of cutter 

Number of teeth 

Pitch diameter 

Outside diameter 

Center distance 

Addendum 

Whole depth 

Spiral angle 

Lead exact 

Lead approximate , 

Number of teeth for which to select 

cutter 

The change gears for cutting this spiral 
are: 

Gear on worm 

First intermediate 

Second intermediate 

Gear on screw 



Small Gear 


Large Gear 


5 


5 


22 


44 


4.722" 


11.278" 


5.122" 


11.678" 


8.000" 


8.000" 


.200" 


.200" 


.4314" 


.4314" 


21° 17' 


38° 43' 


38.081" 


44.198" 


38.182" 


43.977" 


27 (No. 4 Cutter) 


115 (No. 2 Cutter) 


72 


86 


24 


44 


56 


72 


44 


32 




Fig. 299 

Cutting a short lead spiral gear on a Plain Miller 



A Treatise on Milling and Milling Machines 341 

The equipment shown in Fig. 299 is a No. 3 Cincinnati Miller 
with Dividing Head and Spiral Milling Attachment. The blank is 
steel, 3" diameter, 3 pitch, 60° spiral, and is fed past the cutter 
1" per minute. This equipment will mill spirals of any angle up to 
about 70°. It will also cut racks. 




Fig. 300 

Cutting a long lead spiral gear. 



Fig. 300 shows a Cincinnati High-Power Universal Miller with 
its regular equipment of Dividing Head, etc. The table may be 
swiveled 52° for either right or left hand spirals. For spirals 
having a larger angle the Spiral Milling Attachment must be used. 



342 The Cincinnati Milling Machine Company 



CHAPTER XVII 
WORM GEARING 

If, in a pair of spiral gears, the driver has a very small number of 
teeth, as for instance, one, two, three or four, and the driven gear 
a proportionately large number; in other words, if the velocity 
ratio is very great then we get a gearing arrangement which is com- 
monly called endless screw or worm gearing. The driver, which is 
called a worm, is a screw with single or multiple threads of such a 
form that its cross section is the same as that of a rack and its 
teeth must mesh with a special form of spur gear called a wormwheel. 

In a worm and wormwheel with shafts at right angles, the teeth 
of the wormwheel form an angle with the shaft which is the same as 
the complement of the spiral angle of the worm; that is, 90° minus 
the spiral angle of the worm. A wormwheel may therefore be a 
plain spur gear with its teeth at an angle with its axis. Such worm- 
wheels are in common use. But the more efficient form of worm- 
wheel used in machinery of the better class has its teeth made to 
fit the worm thread accurately. This is the form of wormwheel that 
should preferably be used wherever efficiency and durability are 
essential. 

The velocity ratio of a worm and wormwheel is independent 
of their relative pitch diameters; if the worm has a single thread 
the velocity ratio is equal to the number of teeth of the wormwheel ; 
with a double-threaded worm it is one-half; with a quadruple- 
threaded worm one-fourth of the number of teeth of the worm- 
wheel, and so on. 

Careful distinction should be made between the terms "pitch" 
and "lead." The distance between the center of two adjacent 
threads is termed the "pitch" or more correctly, the "linear pitch," 
while the "lead" is the distance which any one thread advances 
in one revolution of the worm. Therefore, the lead and pitch 
of any single-threaded worm will be equal, while for a double- 
threaded worm the lead is twice, and for a quadruple-threaded 
worm four times the linear pitch, and so on. 



A Treatise on Milling and Milling Machines 343 



Worm threads, that is, the teeth of a worm, have straight sides 
at an included angle of 29°, Fig. 301. 

The Worm Cutting Tool. The width at the end of the lathe 
tool used for chasing a worm, or the width of the top of the tooth 
of the cutter when the worm thread is milled, equals the linear 
pitch P* of the worm multiplied by .31. This is also the width of 
the bottom of the space between the threads. We have, therefore 



Width of cutting tool at end = P x .31. 

The included angle between the sides of the tool 



29°. 



Liner* Pitch* P 
If 



-.335 P 




For Double. Threod 



Fig. 301 



The full depth or cutting depth of the worm thread = P x . 6866. 

A worm cut to this depth with a correct tool will have a width 
at top of thread = P x .335. 

The Outside Diameter. The outside diameter of the worm 
blank is obtained by adding twice the addendum to the pitch 
diameter. 

P 



The addendum S = P x .3183 or 



3 . 14159 
The outside diameter o = P + 2S. 

The accompanying table gives the important dimensions of 
worm thread parts. 

*P is linear pitch of worm and circular pitch of wheel, therefore, all these 
calculations are based on circular pitch. 



344 



The Cincinnati Milling Machine Company 




Fig. 302 



To compute the necessary dimensions for a worm gear drive, 
the following formulas should be used in connection with Figs. 
301 and 302. 

P = circular pitch of wheel and linear pitch of worm. 

I = lead of worm. 

n = number of threads in worm. 

S = addendum. 

d = pitch diameter of worm. 
D = pitch diameter of wormwheel. 

o = outside diameter of worm. 

O = throat diameter of wormwheel. 

O' = diameter of wormwheel over sharp corners. 

b = bottom diameter of worm. 
N = number of teeth in wormwheel. 
W = whole depth of worm tooth. 
T = width of thread tool at end. 
B = helix angle of worm. 
— B = gashing angle of wormwheel. 

U = radius of curvature of wormwheel throat 
C = center distance. 



A Treatise on Milling and Milling Machines 345 



Rules and Formulas for Worm Gearing 



To Find 


Rule Formula 


Linear Pitch 


Divide the lead by the number of threads. 
It is understood that by the number of 
threads is meant, not number of threads 
per inch, but the number of threads in 
the whole worm — one, if it is single- 
threaded; four, if it is quadruple-thread- 
ed, etc 


1 
P = - 

n 








Addendum of 
Worm Tooth 


Multiply the linear pitch by 0.3183 


S = 0.3183 P 


Pitch Diame- 
ter of Worm 


Subtract twice the addendum from the 
outside diameter 


d = o - 2 S 


Pitch Diame- 
ter of Worm- 
wheel 


Multiply the number of teeth in the wheel 
by the linear pitch of the worm, and 
divide the product by 3 . 1416 


NP 

D = 

3.1416 


Center Dis- 
tance Be- 
tween Worm 
and Gear 


Add together the pitch diameter of the 
worm and the pitch diameter of the 
wormwheel, and divide the sum by 2 ... . 


D + d 

2 


Whole Depth 
of Worm 
Tooth 


Multiply the linear pitch by . 6866 


W = 0.6866 P 


Bottom Di- 
ameter of 


Subtract twice the whole depth of tooth 
from the outside diameter 


b = o - 2 W 


Worm 






Helix Angle 
of Worm 


Multiply the pitch diameter of the worm 
by 3. 1416, and divide the product by the 
lead; the quotient is the tangent of the 
helix angle of the worm 


Tan B = 
3.1416 d 

I 


Width of 
Thread Tool 
at End 


Multiply the linear pitch by 0.31 


T = 0.31 P 


Throat Di- 
ameter of 
Wormwheel 


Add twice the addendum of the worm 
tooth to the pitch diameter of the worm- 
wheel 


O = D + 2 S 


Radius of 
Wormwheel 
Throat 


Subtract twice the addendum of the worm 
tooth from half the outside diameter of 
the worm 



U = 2 S 

2 


Outside Di- 
ameter of 
Worm 


Add together the pitch diameter and 
twice the addendum 


o = d + 2 S 


Pitch Diame- 
ter of Worm 


Subtract the pitch diameter of the worm- 
wheel from twice the center distance. . . . 


d = 2 C - D 


Diameter of 
Wormwheel 
to Sharp 
Corners 


Multiply the radius of curvature of the 
wormwheel throat by the cosine of half 
the face angle, subtract this quantity 
from the radius of curvature, multiply the 
remainder by 2, and add the product to 
the throat diameter of the wormwheel . . . 


O' = 2 (C7 -- U X 

cos - ) +0 
2/ 


Gashing Angle 
of Gear 


Divide the lead of the worm by the cir- 
cumference of the pitch circle. The 
result will be the tangent of the gashing 
anele 


Tan (90° -B) = 

1 

x d 



346 



The Cincinnati Milling Machine Company 



Table of Important Dimensions of Worm Thread Parts 





Circular 


Circ. or 


Height 


Depth 




Thick- 


Width of 




No. of 


or Linear 


Linear 


of Tooth of Space 


Whole 


nesa of 


Thread 


Width of 


Threads 


Pitch, 


Pitch, 


above 


below 


Depth of 


Tooth on 


Tool 


Thread 


per In. 


Inches 


Decimal 
Eqaiva 


Pitch 

L::lt 


Pitch 

Lir.e 


Tooth 


Pitch 

Line 


at End 


at Top 


i 


2 


2.0000 


0.6366 


0.7366 


1.3732 


1.0000 


0.6200 


0.6708 


4 


m 


1.7500 


0.5570 


0.6445 


1 . 2015 


Q -750 


0.5425 


0.5869 


i 

3 


m 


1.5000 


0.4775 


0.5524 


1 . 0299 


■". :// 


0.4650 


: //.: 


4 

9 


m 


1.2500 


0.3979 


0.4603 


S582 


0.625C 


0.3875 


0.4192 


1 


i 


1.0000 


0.3183 


0.3683 


0.6866 


0.5000 


0.3100 


0.3354 


m 


s 


0.7500 


0.23S7 


0.2762 


0.5149 


0.3750 


0.2325 


0.2515 


m 


2 

3 


0.6667 


0.2122 


0.2455 


0.4.57; 


0.3333 


: :<>;■-: 


: __■ 


2 


1 
g 


0.5000 


0.1592 


0.1841 


0.3433 


0.2500 


0.1550 


0.1677 


2Y 2 


2. 

5 


0.4000 


0.1273 


0.1473 


0.2746 


0.2000 


0.1240 


0.1341 


3 


1 
3 


0.3333 


0.1061 


0.1228 


0.2289 


0.1667 


0.1033 


0.1118 


3H 


2 


0.2857 


0.0909 


0.1053 


. 1962 


0.1429 


0.0886 


'. >V-58 


4 


1 

4 


0.2500 


0.0796 


0.0920 


0.1716 


0.1250 


0.0775 


'.' O-o'*- 


43^ 


2 
9 


0.2222 


0.0707 


0.0819 


0.1526 


0.1111 


0689 


0.0745 


5 


1 

5 


0.2000 


0.0637 


0.0736 


0.1373 


0.1000 


0.0620 


0.0670 


6 


1 
6 


0.1667 


0.0531 


0.0613 


0.1144 


0.0833 


0.0511 


a //- 


7 


1 


0.1429 


0.0455 


0.0526 


0.0981 


0.0714 


0.0443 


0.0479 


8 


1 

8 


0.1250 


0.0398 


0.0460 


0.0858 


0.0625 


0.08-7 


0.0419 


9 


£ 


0.1111 


0.0354 


0.0409 


0.0763 


0.0556 


0.0344 


0.0373 


10 


1 
10 


0.1000 


0.0318 


0.0369 


0.0687 


0.0500 


0.0310 


0.0335 


12 


1 
12 


0.0833 


0.0265 


0.0307 


0.0572 


0.0416 


0.0258 


0.027S 


14 


1 
ME 


0.0714 


0.0227 


0.0263 


0.0490 


0.0357 


0.0221 


0.0239 


16 


1 

1 5 


0.0625 


0.0199 


0.0230 


0.0429 


0.0312 


0.0194 


02'"/:' 


18 


1 

or 


0.0556 


0.0177 


0.0205 


0.03S2 


0.0278 


0.0172 


0.01/ 



Practical Example. When computing a worm and wormwheel 
it is customary to assume the outside diameter of the worm if 
possible make it so you can use an existing hob and the linear 
pitch. The velocity ratio is, of course, given. 

We will take for our example a single-threaded worm, two 
threads per inch. The linear pitch is therefore }o'. Assume the 
outside diameter to be 2 .000" and the velocity ratio 40 to 1. 

As the worm is single threaded, n - 1. Therefore, 



Z=Pxn = ^xl = 



(The lead equals the linear pitch in 



this case, since the worm is single threaded., 

S = .3183 xP= .3183 x .5 = .15915". 

d = 2 - (2 x .15915.; = 2 - .3183 = 1.6817". 



D = 



P x X 40 / .5 



20 



3.1416 



3.1416 3.1416 



= 6.3662". 



A Treatise on Milling and Milling Machines 347 
C = D + d = y 2 (6.3662 + 1.6817) = 4.0239. 

Li 

w = .6866 x P - .6866 x .5 = .3433. 

b = o-2w = 2-(2x .3433) = 2 - .6866 = 1.3134. 

™ . -d x x d 3.1416 x 1.6817 1A ccc . ,, , 

Tangent B = = = 10.5564 therefore, 

1 .5 

B = 84°36', the helix angle of worm. 

The gashing angle of wormwheel (90° — B) = 5°24'. 

T = .31 x P = .31 x .5= .155", the width of thread tool at 
end. 

= D + 2 + S = 6.3662 + .3183 = 6.6845", the throat diame- 
ter of the wormwheel. 

Cutting the Wormwheel. Cutting a wormwheel on a Milling 
Machine requires two operations ; first, gashing the teeth, and second, 
hobbing the teeth to correct size and shape. 

The gashing operation consists of roughing out the gear teeth. 
The cutter should be an involute cutter of the same diameter and 
pitch as the worm threads. 

The wormwheel to be gashed is held between centers, Fig. 303, 
and the table of the machine is moved longitudinally to bring the 
cutter central over the work, having first made sure that the cutter 
is central with the dividing head center, as when cutting spur gears; 
then the milling machine table is swiveled to an angle corresponding 
with the gashing angle. For worm wheels driven by a right-hand 
worm, that is, wheels finished by a right hand hob, swivel the 
milling machine table toward your right hand (when facing 
either end of the table), and for worm wheels driven by left- 
hand worms, swivel it to the left. The work is fed vertically 
into the cutter to the desired depth for each tooth. The work 
is indexed the same as a spur gear. This gashing operation should 
be carried out so as to leave only a small amount of metal on the 
sides and bottom of the teeth for the final finishing or hobbing opera- 
tion. 

The Gashing Angle. The gashing angle for the gear depends 
on the diameter and lead of the WORM. It is found by dividing the 
lead of the worm by the circumference of its pitch circle which gives 
the tangent of the desired angle. 



348 



The Cincinnati Milling Machine Company 




Fig. 303 

Gashing a wormwheel. Table is swiveled the amount of the gashing angle, and the work is fed ver- 
tically to the cutter. 



m i? i • i Lead of worm 
langent of gashing angle = ; 

Circumference of pitch circle 



that is, 



tan (90° -B) = 



x d 



The angle may then be read from a table of natural tangents. 
The gashing angles for wormwheels for a variety of worms from 
Y% to 6" diameter and from Vio" to 1^2" lead may be taken directly 
from the table at the end of this chapter. 

For example: Suppose we have a worm 3" pitch diameter, y{ 
lead or two threads per inch, which is the same thing. We find in 
the column opposite Y^' lead and under 3" P. D., 3°2 / , which is the 
gashing angle for the gear that will work with that worm. 



A Treatise on Milling and Milling Machines 349 

Hobbing the Wormwheel. For the hobbing operation the 
wormwheel must be so held between centers that it can revolve 
freely, because it must be driven by the hob. If the worm and 
wormwheel have shafts at right angles (which is the usual form) 
the table of the milling machine must be set straight; that is, at 
right angles with the cutter arbor, Fig. 304. 

The gashing cutter must be replaced by a hob of proper size 
and pitch. The hob must, of course, be central over the rim of the 
wormwheel and the table should be locked in position to insure 




Fig. 304 

Hobbing a wormwheel. 



against movement. When the machine has been started, raise the 
knee until the hob has cut to the proper depth. If excessive stock 
has been left to be removed, or if an exceptionally good finish is 
wanted, it is best to revolve the wormwheel under the hob a number 
of times, bringing it to final finish depth for the last cut or revolution. 

Special hobbing attachments are sometimes provided for the 
milling machine, which are arranged for positively driving the work 



350 



The Cincinnati Milling Machine Company 



spindle by means of gears from the machine spindle so as to insure 
positive rotation of the gear in exactly the correct ratio with the 
hob. With such an attachment the preliminary gashing operation 
can be omitted. 

Gashing Angles for Wormwheels 



Lead 
of 


No. of 
Thr'ds 
per In. 

in 
Worm 


PITCH DIAMETER OF WORM 


Wrm. 
in In. 


h A % 


% 


1 


VA 


va ' m 


v/ 2 1 m 


VA VA 


2 ! 2A 


2M 


2A 


2V 2 


1/10 

1/9 

1/8 

1/7 

1/6 

1/5 

1/4 

2/7 

1/3 

4/11 

3/8 

2/5 

4/9 


10 

9 
8 
7 
6 
5 
4 

VA 

3 

2% 
2% 
2A 
2M 
2 

1M 

VA 
VA 
VA 
1 

Z A 
A 


2°55' 

3°14' 

3°3S' 

4° 10' 

4°51' 

5°49' 

7° 16' 

8°17' 

9°38' 

10°30' 

10°49' 

11°31' 


2°26' 
2°42' 
3° 2' 
3°28' 
4° 3' 
4°51' 
6° 4' 
6°55' 
8° 3' 
8°46' 
9° 3' 
9°38' 


2° 5' 
2°19' 
2°36' 
2°58' 
3°28' 
4°10' 
5°12' 
5°56' 
6°55' 
7°32' 
7°46' 
8°17' 


1°49' 
2° 1' 
2°17' 
2°36' 
3° 2' 
3°39' 
4°33' 
5° 12' 
6° 3' 
6°36' 
6°48' 
7°15' 
8° 3' 


1°37' 
1°48' 
2° 2' 
2°19' 
2°42' 
3°14' 
4° 3' 
4°37' 
5°23' 
5°52' 
6° 4' 
6°27' 
7°10' 


1°28' 
1°37' 
1°49' 
2° 5' 
2°26' 
2°55' 
3°39' 
4°10' 
4°51' 
5°17' 
5°27' 
5°49' 
6°27' 
7°15' 


1°20' 
1°28' 
1°39' 
1°54' 
2°13' 
2°39' 
3°19' 
3°47' 
4°25' 
4°49' 
4°58' 
5°17' 
5°52' 


1°13' 
1°21' 
1°31' 
1°44' 
2° 1' 
2°26' 
3° 2' 
3°28' 
4° 3' 
4°25' 
4°33' 
4°51' 
5°23' 


1° 7' 1° 2' 
l°15'i 1° 9' 
1°24'' 1°18' 
l°36'i 1°29' 
l°52'i 1°44' 
2°15'| 2° 5' 
2°48'i 2°36' 
3°12'j 2°58' 
3°44'; 3°28' 
4° 4' 3°47' 
4°12' 3°54' 
4°29' 4°10' 
4°59' 4°37' 


58' 
1° 5' 
1°13' 
1°23' 
1°37' 
1°57' 
2°26' 
2°47' 
3°14' 
3°32' 
3°39' 
3°53' 
4°19' 


55' 
1° 1' 
1° 8' 
1°18' 
1°31' 
1°49' 
2°17' 
2°36' 
3° 2' 
3°19' 
3°25' 
3°39' 
4° 3' 


52' 

57' 
1° 4' 
1°14' 
1°26' 
1°43' 
2° 9' 
2°27' 
2°52' 
3° 7' 
3°13' 
3°26' 
3°46' 
4°17' 
4°54' 
5°42' 
6°25' 


49' 
54' 
1° 1' 
1° 9' 
1°21' 
1°37' 
2° 2' 
2°19' 
2°42' 
2°57' 
3° 2' 
3°14' 
3°36' 
4° 3' 
4°37' 
5°23' 
6° 3' 


46' 
51' 
58' 
1° 6' 
1°17' 
1°32' 
1°55' 
2°12' 
2°33' 
2°47' 
2°53' 
3° 4' 
3°25' 


44' 
49' 
54' 
1° 3' 
1°13' 
1°27 
1°49' 
2° 5' 
2°26' 
2°39' 
2°44' 
2°55' 
3° 14' 


1/2 








6°36' 6° 3' 


5°36' 5°12' 


4°51' 4°33' 
5°32' 5° 12' 


3°50' 3°39' 


4/7 














6°55' 


6°23' 


5°56' 


4°23' 4°10' 


2/3 




















6°27' 


6° 3' 


5° 6' 4°51' 


3/4 




















5°44' 5°27' 


4/5 
























6° 7' 5°49' 


1 































VA 






























V-A 





























































Lead 
of 


No. of 
Thr'ds 
per In. 

in 
Worm 


PITCH DIAMETER OF WORM 


Wrm. 
in In. 


2 5 A 


2% 


2V S 


3 


VA 


VA 


m 


4 


VA 


4M 


4M 


5 


5M 


5H 


5M 


6 


1/10 


10 
9 
8 
7 
6 
5 
4 

VA 
3 

2H 
2A 
2A 

2M 

2 

VA 
VA 
VA 
VA 
l 

U 
A 


































1/9 
1/8 


































52' 

1° 
1° 9' 

1°23' 
1°44' 
1°59' 
2°19' 
2°31' 
2°36' 
2°47' 
3° 5' 
3°28' 
3°58' 
4°37' 
5°12' 
5°32' 
6°55' 


50' 
57' 

1° 6' 
1°20' 
1°39' 
1°54' 
2°13' 
2°25' 
2°29' 
2°39' 
2°57' 
3°19' 
3°47' 
4°25' 
4°58' 
5°17' 
6°36' 


48' 
54' 
1° 3' 
1°16' 
1°35' 
1°49' 
2° 7' 
2°18' 
2°23' 
2°32' 
2°49' 
3°10' 
3°37' 
4° 13' 
4°45' 
5° 4' 
6°19' 
8°24' 


46' 
52' 
1° 1' 
1°13' 
1°31' 
1°44' 
2° 2' 
2°13' 
2°17' 
2°26' 
2°42' 
3° 2' 
3°28' 
4° 3' 
4°33' 
4°51' 
6° 3' 
8° 3' 
9° 3' 


42' 
48' 
56' 
1° 7' 
1°24' 
1°36' 
1°52' 
2° 2' 
2° 6' 
2° 14' 
2°30' 
2°48' 
3°12' 
3°44' 
4°12' 
4°29' 
5°36' 
7°26' 
8°22' 


39' 

45' 

52' 

1° 3' 

1°18' 
1°29' 
1°44' 
1°54' 
1°57' 
2° 5' 
2°19' 
2°36' 
2°59' 
3°28' 
3°54' 
4°10' 
5°12' 
6°54' 


36' 
42' 

48' 
58' 
1°13' 
1°23' 
1°37' 
1°46' 
1°49' 
1°57' 
2°10' 
2°26' 
2°47' 
3°14' 
3°39' 
3°53' 
4°51' 
fi°?7' 


34' 
39' 
46' 
55' 
1° 8' 
1°18' 
1°31' 
1°39' 
1°43' 
1°49' 
2° 2' 
2°17' 
2°36' 
3° 2' 
3°25' 
3°39' 
4°33' 
6° 4' 
6°49' 


32' 
37' 
43' 
52' 
1° 4' 
1°14' 
1°26' 
1°34' 
1°37' 
1°43' 
1°54' 
2° 9' 
2°27' 
2°52' 
3°13' 
3°26' 
4°17' 
5°42' 
6°26' 
















1/7 


35' 
40' 
49' 
1° 1' 
1° 9' 
1°21' 
1°28' 
1°31' 
1°37' 
1°48' 
2° 2' 
2°19' 
2°42' 
3° 2' 
3°14' 
4° 3' 
5°23' 
6° 4' 


33' 
38' 
46' 
58' 
1° 6' 
1°17' 
1°24' 
1°26' 
1°32' 
1°42' 
1°55' 
2°12' 
2°33' 
2°53' 
3° 4' 
3°50' 
5° 6' 
6°44' 












1/6 
1/5 
1/4 
2/7 
1/3 
4/11 
3/8 
2/5 
4/9 
1/2 
4/7 
2/3 
3/4 
4/5 
1 
VA 


36' 

44' 
55' 

1° 3' 
1°13' 
1°20' 
1°22' 
1°28' 
1°37' 
1°49' 
2° 5' 
2°26' 
2°44' 
2°55' 
3°39' 
4°51' 


35' 
42' 
52' 
1° 1' 
1° 9' 
1°16' 
1°18' 
1°23' 
1°33' 
1°44' 
1°59' 
2°19' 
2°36' 
2°47' 
3°28' 
4°37' 








40' 
50' 
57' 
1° 6' 
1°12' 
1°15' 
1°20' 
1°28' 
1°39' 
1°54' 
2°13' 
2°29' 
2°39' 
3°19' 
4°25' 
4°58' 


38' 
48' 
54' 
1° 3' 
1° 9' 
1°11' 
1°16' 
1°24' 
1°35' 
1°49' 
2° 7' 
2°23' 
2°32' 
3° 10' 
4°13' 


46' 
52' 
1° 1' 
1° 6' 
1° 8' 
1°13' 
1°21' 
1°31' 
1°44' 
2° 1' 
2°17' 
2°26' 
3° 2' 
4° 2' 


VA 






7°46' 7°15' 


5°27' 5°12' 


4°45'l 4°3c 





















A Treatise on Milling and Milling Machines 351 



CHAPTER XVIII 

CONTINUED FRACTIONS 
ANGULAR INDEXING 

Angular Indexing. The tables on pages 329-30-31 will be 
found convenient for angular indexing when it is desired to space 
holes or notches a given number of degrees and minutes apart. 
These tables contain all that is required in the great majority of 
cases. They give angles that may be obtained with the index plate 
regularly furnished with the Cincinnati Universal Dividing Head 
and are accurate to within one-half a minute, with the exception 
of those few in heavy type. In these the error is somewhat 
greater and may amount to a minute or slightly more. The tables 
give angles advancing by minutes from 3' up to 9°, which corres- 
ponds to one full turn of the index handle. For larger angles we 
make one full turn for each 9° plus the reading in the table cor- 
responding to the fractional degrees and minutes. For example, 
to index spaces 20°15' apart, two turns give an 18° space, and for 
the 2° 15' we find in the table a spacing of 7 holes in the 28 circle. 
The entire spacing is, therefore, using the 28 circle, 2 turns 7 holes. 
When it is desired to space angles to closer limits than those given 
in the tables the spacing can be computed by following the com- 
paratively simple method of Continued Fractions described below. 

Computing the Spacing. Suppose the drawing comes to the 
shop showing a spacing of 37°34'29", and the nature of the work 
makes it desirable to come as close to this as is practical with a 
Universal Dividing Head. 

One turn of the index crank produces an angle of 9° because 40 
turns produce one complete turn of the spindle, or 360°. We note 
right away that we can make four complete turns which makes 
36° and there is left an angle of 1°34'29". The question is now, 
what circle of holes shall we use and how many spaces should be 
indexed. One complete turn of the index crank makes 9°, or 32400 ". 
We must make an angle of 1° (which is 3600 seconds), 34' (which is 
2040 seconds), and 29", or altogether 5669". It is, therefore, 



352 The Cincinnati Milling Machine Company 

5669 

necessary to make of a full turn of the index crank. This 

32400 

would be easy enough if we had a circle with 32,400 holes, but, of 
course, this is not the case. We must, therefore, find some other 
fraction which has a much smaller denominator and a value very 
close to the given fraction. If we can find one in which the denomi- 
nator is the number of holes in one of the circles, we have an easy 
way of spacing this angle. 

Greatest Common Divisor. If two numbers have a common 
divisor, such, for instance, as 21 and 77, which have the common 
divisor 7, then, if we should subtract 21 from 77 the remainder will 
also have this divisor 7 as a factor; and if we subtract several times 
21 from 77 that remainder also has the factor 7; in other words, 
if 21 and 77 have a common divisor, and we should divide 21 into 
77, the remainder of the division can also be divided by 7. If then 
we should divide this remainder into the 21, the remainder of this 
new division would also have this factor 7. We could keep this up, 
always dividing the remainder of the last division into the divisor 
of this last division, until finally the division would leave no remain- 
der, then the last divisor would be the greatest common divisor. 

2!)77(3 

1-4) 21 ( I 
_±4 
~~7") 14(2 

JL± 

o 

Seven being the last divisor is the greatest common divisor. 

Continued Fractions. In the following example, we will 

943 
assume a fraction . Here we will find that there is no greatest 

1727 
common divisor. 



A Treatise on Milling and Milling Machines 353 



943) 1727 ( I 
943 

784)943 ( i 
784.' 

I 59)784(4 
636 

I ^8 ) 159 ( I 
148 
I 1)148 (13 



38 
33 
5)11(2 
IP , 
1)5(5 

o 



We will now show how it would be possible to find the original 
figures, 943 and 1727, if nothing but the quotients were given. We 
know that the last divisor was 1, the remainder is and the quo- 
tient is 5, therefore the dividend must have been five times 1, or 5. 
The previous divisor, therefore, is also 5. The quotient was 2 and 
the remainder was 1, so we find that the dividend there must have 
been 2 times 5 plus 1 equals 11. The previous divisor, therefore, 
was 11, and the dividend was 13 times 11 plus 5 equals 148. Con- 
sequently, the previous divisor was 148. We could go on this way 
by always multiplying the last quotient by the last divisor and adding 
the last remainder, and using this resulting number as the previous 
divisor. But there is a much simpler way of doing this very thing. 

Prepare a diagram as in Fig. 305 and place the quotients from 
our continued fraction in the spaces above the line from left to right 
beginning with the last quotient. 




In the spaces below the line, but beginning two spaces to the left 
of the last quotient we write 0, which was the last remainder, and 
to the right of it 1, which was the last divisor. 



354 



The Cincinnati Milling Machine Company 



By following a system of multiplication and addition, as indi- 
cated above, by following the arrows in Fig. 305, we get 5x1 + = 5, 
which was the next to the last divisor. This is placed in the space 
to the right of the last divisor, which brings it below the last quo- 
tient. In the same way 2 x 5 + 1 = 11 and 13 x 11 + 5 = 148, 
1 x 148 + 11 = 159 and so on until we finally get back to the original 
numbers 943 and 1727. 

Now it is a peculiar property of numbers that, if we should cut 
off part of this operation, say along the line A; in other words, if 
we should start with 13 instead of 5, making a diagram as in Fig. 
306, we will get another fraction but which is very close in value 
to the original fraction. 



13 







13 14 69 

Fig. 306 



152 



Another peculiar property of numbers is that if we should cut 
off at A and find that the resulting fraction is a little too large, 
then, if we cut off at C, one place further to the right, the fraction 
would be a little too small, and if we should start at E the fraction 
would be too large again, and so on. The value of these approxi- 
mating fractions would move somewhat like the wave line in Fig. 307. 




Fig. 307 

The straight line represents the true value of our original frac- 
tion and the wave line represents the value of the approximating 
fractions. It will be seen that these approximating fractions go 
alternately above and below the real value and that they gradually 
go farther and farther away from that value. 

The diagram, Fig. 306, shows that the resulting fraction if we 

83 



started on the line A would be 



152 



If we reduce the original frac- 



tion 



943 
1727 



to a decimal fraction we get .54603, and reducing the 



A Treatise on Milling and Milling Machines 355 



83 
approximate fraction we get .54605, or a difference of .00002. 

In other words, we have an error of 2 in a total of 54600, which is a 
very small error indeed. If this fraction had been used for spacing, 
the holes or notches thus spaced might have been nearly 53^ v apart 
with an error of only .0002. Returning now to our problem of 

spacing . We carry a continuous division, 

32400 



5669)32400(5 
28345 , 
4055)5669(1 
4055 

1614)4055(2 
3228 , 

"~527)l6l4(| 
_827 

787)827(i 
787 

40)787 (l 9 
4Q 
387 
360 N 

~27)40(i 
27 
13)27(2 

I )l3(l3 

13. 

O 



just like in the previous example and then we ignore the last four 
quotients, keeping only the quotients 5, 1, 2, 1 and 1, Fig. 308. 







2 

Fig. 308 



40 



We set these five quotients up in our diagram as before, and find 



the approximate fraction — , which means that we have to take 

7 7 7 

7 spaces on the 40 hole circle. - of a circle is — of 9°, or — of 32400 

40 40 40 



356 



The Cincinnati Milling Machine Company 



seconds. This is 5670 seconds, whereas what we want is 5669 
seconds. This shows that we have missed our angle by one second. 
However, we meet a new difficulty here. We find that we must 
take 7 spaces on a 40 hole circle, but there is no such circle on the 
standard index plate. If there should be great need of extreme 
accuracy a special plate with a 40 hole circle could be made, but, 
as a rule, the accuracy required is not so great, nor would the dividing 
head permit of such extreme accuracy as an error of less than one 
second. Such extreme accuracy is only found in the most refined 
astronomical instruments and has no place in the machine shop. 
Instead, then, of making a special plate with a 40 hole circle we cut 
off the next quotient, leaving only the quotients 1, 2, 1 and 5, Fig. 
309. 







1 


2 


1 


5 




1 


3 

Fig. 309 


4 


23 





This will give us the fraction — , and this is easily obtainable 

4 
by using the 46 hole circle and taking 8 spaces. — of 9° gives us 

Zo 

5635 seconds, whereas we wanted 5669 seconds, so that our space 
is 34 seconds too small. Even this is a high degree of accuracy, 



the error being only about — of what it would be with the ordinary 

method of circular indexing. 

We could have cut off still another quotient and used only the 

3 



figures 2, 1 and 5, in which case we would have found the fraction 
Fig. 265. 



17' 







2 

Fig. 310 



17 



This means that we would have had to use the 34 hole circle 
and take 6 spaces. The result would have been 5717 instead of 
5669 seconds, or an error of 48 seconds. Even this is a great im- 
provement over the regular method. You will note that with five 



A Treatise on Milling and Milling Machines 357 

quotients we were 1 second LARGE; with four quotients 34 seconds 
small; and with three quotients we were 48 seconds large.* 

The method of continued fractions is useful in a great many other 
instances, of which two examples are given. 

Application to Gearing a Lathe to Gut Metric Threads. 

We know that if we have a standard lead screw on a lathe and 
want to cut metric threads we must introduce a pair of compound 
gears which will make up for the difference between metric and 
English pitches. If, for instance, we have a }/i" pitch lead screw and 
want the lathe to work as if the pitch of the screw were 6 millimeters, 
we put a pair of compound gears in the feed mechanism of 120 and 
127 teeth respectively. If the pitch of the lead screw is 3^" and we 
want to make the lathe work as if the lead screw had a pitch of 10 
millimeters, we introduce a pair of compound gears of 100 and 127 
teeth respectively. Now, such gears of 100 and 127 teeth are quite 
large and it will generally be found that it is impractical to put such 
gears into an existing mechanism. The numbers 100 and 127 are 
relatively prime and it is not possible to find another fraction of 
the same value by canceling. We resort, therefore, to our method 
of continued fractions. We make the continuous division of 100 
and 127 and ignore first one and then perhaps two or more of the 
last quotients until we find a fraction which is sufficiently small, 
and then we test this fraction for its accuracy. Ignoring the last 

37 
quotient we obtain the fraction — , which means that we will have 

47 

to use two gears of 37 and 47 teeth respectively. These numbers 
are quite practical and it should be easy to introduce a pair of gears 
of that size into a mechanism. In order to test out the accuracy 

*It does not matter which of the two numbers comprising a fraction is 
divided into the other. It is simplest to divide the smaller into the larger 
to avoid decimals. However, in arranging the figures composing our new 
equivalent fraction we must remember that 

b. If we use the denominator as a divisor, the last divisor produced becomes 
the numerator of our equivalent fraction since the natural relation is not 
disturbed. 

c. If we use the numerator as the divisor, which happens to be the case 
in the examples given here, we have reversed the natural relation and now the 
last divisor produced becomes the denominator of the equivalent fraction, thus, 

943 83 

— , 943)1727( = - 



358 The Cincinnati Milling Machine Company 



100 37 

of this fraction we reduce and — to decimal fractions and find 

127 47 

that there is a difference of 17 in a total of 78740, which is quite 
accurate enough for all but the very finest work. If we had cut 
off one more quotient we would have found the approximating 

fraction — , which is quite convenient, but not quite so accurate. 

oo 

The error in this case is 48 in a total of 78740; in other words, 

nearly three times as much as with the fraction — . 

47 

Application to Computing Change Gears for Cutting 
Spirals. Another application of this method is to be found in com- 
puting the change gears required to cut a spiral of given lead. A 
Dividing Head is furnished with a certain number of change gears 
which are quite sufficient for all ordinary work, and this book 
contains a table of the leads which can be cut with these change 
gears. The teeth in reamers, taps, cutters, etc., can easily be cut 
with these change gears. Even spiral gears can, as a rule, be cut 
without using any other change gears than the ones supplied. How- 
ever, some times spiral gears must be cut with great accuracy and 
a relatively small variation in the lead is not permissible. In Chapter 
XVI, on spiral gear cutting, we showed that the lead is found by 
the simple formula: 

T , pitch circumference 

Lead = - 

tangent of spiral angle 

and from this it follows that the lead is usually a decimal fraction 
and it would be strange indeed if this fraction could always be found 
in the table of leads. 

Assume that we have to cut a spiral gear having a lead of 5 . 8042 ". 
Consulting our table of leads we find that the nearest leads given 
are 5.788 and 5.833. Neither of these two leads is close enough 

- , , . ,, driven gears lead* £ 

for very accurate work. Since the = our frac- 

driving gears 10 

tion is — . This is an awkward fraction to reduce into suitable 

10 

form for conversion into change gears. We will therefore carry out 
our method of continued fractions. For convenience we multiply 

*See Chapter XIX. 



A Treatise on Milling and Milling Machines 359 



both numerator and denominator by 10,000 in order to get rid of 
the decimal. This, of course, does not change the value of the 

58042 



fraction, which now is 



We now have 



100000 



58042)lO0OOo(l 
58042 

^1958)58042(1 
4l958 v 

16084)41958(2 

32168 



9790)l6O84(| 
9790 

6294)9790(1 
6294- 

3496)6294(1 
3496 

2798)3496(1 
2798 
698)2798(4 
2792. 

6)698(116 
6_ 
9 

6_ 
38 
36 
2)6(3 
6 
O 



Dropping the last three quotients and applying our diagram, 
we get 







1 


1 1 


1 


2 


1 


1 


2 


4 6 


10 


26 


36 


62 



Our approximately equivalent fraction is therefore 



36 
62' 



Testing 



this for accuracy, we divide 62 into 36, which gives us .580645. 
However, we must remember that we started with a fraction which 
represented the lead divided by 10. This approximate equivalent 
is therefore also tV of the lead. Multiplying it by 10 we therefore 



360 The Cincinnati Milling Machine Company 

get 5.80645 as our approximate lead, which compared with the 
actual lead of 5.8042 shows that our new approximation is . 00225 " 
long. This, however, is so small an error that it is not likely to lead 
into difficulties. 

We will, therefore, split up our fraction — and convert it into 

62 



suitable change gears. Thus 




36 4x9 




62 6.2 x 10 




4 10 40 9 6 
6.2 " 10 " 62' 10 > 6 


54 
~ 60 



Our change gears therefore are 

40 x 54 driven gears 2d Intermediate x Gear on worm 
62 x 60 driving gears 1st Intermediate x Gear for screw 

We therefore put the 40 tooth gear on the second intermediate 
stud, the 54 tooth gear on the worm shaft, the 62 tooth gear on the 
first intermediate stud, and the 60 tooth gear on the stud in the 
segment, which runs at the same speed as the screw. 



A Treatise on Milling and Milling Machines 361 



Table for Angular Indexing on the Universal Dividing Head 



00 
U 

<u 


00 

3 


JU 


a> 


00 

a> 


oo 

3 


JK 




00 

3 

a> 


CO 
0) 

3 


^0J 


0J 


w 

CD 


09 
0) 
-t-s 

3 


J32 


0J 


Q 


a 


IS 

H 

b 


o3 
GO 


Q 




1j 

t-H 

o 


o3 
GO 


faD 
O 

Q 




b 


03 

GO 


faB 

Q 


a 




03 
(X 
GO 





1 

2 
3 











53 
54 
55 


51 

30 
59 


5 
3 
6 




45 
46 
47 


41 
51 
30 


8 

10 

6 


2 

2 
2 


37 

38 
39 


62 
41 
51 


~J8~ 









12 





181 




15 





4 


137 







56 


58 


6 




48 


30 


6 


2 


40 


54 


16 





5 


107 







57 


57 


6 




49 


54 


11 


2 


41 


47 


14 





6 


181 







58 


28 


3 




50 


54 


11 


2 


42 


30 


9 





7 


77 







59 


46 


5 




51 


34 


7 


2 


43 


53 


16 





8 


66 









54 


6 




52 


53 


11 


2 


44 


66 


20 





9 


59 






1 


62 


7 




53 


43 


9 


2 


45 


59 


18 





10 


54 






2 


43 


5 




54 


57 


12 


2 


46 


39 


12 





11 


49 






3 


43 


5 




55 


47 


10 


2 


47 


42 


13 





12 


46 






4 


59 


7 




56 


28 


6 


2 


48 


58 


18 





13 


42 






5 


25 


3 




57 


37 


8 


2 


49 


51 


16 





14 


39 






6 


49 


6 




58 


59 


13 


2 


50 


54 


17 





15 


37 






7 


24 


3 




59 


59 


13 


2 


51 


41 


13 





16 


34 






8 


24 


3 


2 





54 


12 


2 


52 


66 


21 





17 


62 


2 




9 


47 


6 


2 


1 


58 


13 


2 


53 


53 


17 





18 


30 


1 




10 


54 


7 


2 


2 


62 


14 


2 


54 


59 


19 





19 


57 


2 




11 


38 


5 


2 


3 


66 


15 


2 


55 


37 


12 





20 


54 


2 




12 


30 


4 


2 


4 


39 


9 


2 


56 


46 


15 





21 


51 


2 




13 


37 


5 


2 


5 


39 


9 


2 


57 


58 


19 





22 


49 


2 




14 


51 


7 


2 


6 


30 


7 


2 


58 


58 


19 





23 


47 


2 




15 


43 


6 


2 


7 


51 


12 


2 


59 


54 


18 





24 


47 


2 




16 


57 


8 


2 


8 


38 


9 


3 





54 


18 





25 


43 


2 




17 


42 


6 


2 


9 


46 


11 


3 


1 


54 


18 





26 


62 


3 




18 


62 


9 


2 


10 


54 


13 


3 


2 


59 


20 





27 


59 


3 




19 


41 


6 


2 


11 


66 


16 


3 


3 


59 


20 





28 


58 


3 




20 


54 


8 


2 


12 


49 


12 


3 


4 


47 


16 





29 


37 


2 




21 


66 


10 


2 


13 


49 


12 


3 


5 


38 


13 





30 


54 


3 




22 


66 


10 


2 


14 


28 


7 


3 


6 


58 


20 





31 


53 


3 




23 


39 


6 


2 


15 


28 


7 


3 


7 


49 


17 





32 


34 


2 




24 


58 


9 


2 


16 


28 


7 


3 


8 


66 


23 





33 


49 


3 




25 


38 


6 


2 


17 


59 


15 


3 


9 


57 


20 





34 


47 


3 




26 


25 


4 


2 


18 


47 


12 


3 


10 


54 


19 





35 


62 


4 




27 


62 


10 


2 


19 


66 


17 


3 


11 


51 


18 





36 


30 


2 




28 


43 


7 


2 


20 


54 


14 


3 


12 


59 


21 





37 


58 


4 




29 


54 


9 


2 


21 


57 


15 


3 


13 


42 


15 





38 


57 


4 




30 


54 


9 


2 


22 


38 


10 


3 


14 


39 


14 





39 


42 


3 




31 


47 


8 


2 


23 


34 


9 


3 


15 


47 


17 





40 


54 


4 




32 


47 


8 


2 


24 


30 


8 


3 


16 


66 


24 





41 


66 


5 




33 


58 


10 


2 


25 


41 


11 


3 


17 


66 


24 





42 


51 


4 




34 


46 


8 


2 


26 


37 


10 


3 


18 


30 


11 





43 


25 


2 




35 


57 


10 


2 


27 


66 


18 


3 


19 


38 


14 





44 


49 


4 




36 


62 


11 


2 


28 


62 


17 


3 


20 


54 


20 





45 


24 


2 




37 


39 


7 


2 


29 


58 


16 


3 


21 


43 


16 





46 


47 


4 




38 


66 


12 


2 


30 


54 


15 


3 


22 


43 


16 





47 


46 


4 




39 


49 


9 


2 


31 


25 


7 


3 


23 


53 


20 





48 


34 


3 




40 


54 


10 


2 


32 


39 


11 


3 


24 


53 


20 





49 


66 


6 




41 


59 


11 


2 


33 


53 


15 


3 


25 


58 


22 





50 


54 


5 




42 


53 


10 


2 


34 


49 


14 


3 


26 


42 


16 





51 


53 


5 




43 


42 


8 


2 


35 


66 


19 


3 


27 


47 


18 





52 


62 


6 




44 


57 


11 


2 


36 


38 


11 


3 


28 


39 


15 



362 



The Cincinnati Milling Machine Company 



Table for Angular Indexing on the Universal Dividing Head 



as 
o 
a> 


00 
O 

3 


J2 





D 
O 


00 



J2 


a> 


00 




F-i 


m 

-*> 

3 


.2 





S3 
O 


03 
O 

3 


jy 


© 




S3 

9 




5 


e3 


bfl 
O 

Q 


a 


5 


C3 


bC 
O 

Q 




"3 

'6 


C2 

a 
w. 


bC 




C 
--* 


"0 

3 




3 


29 


62 


24 


4 


21 


62 


30 


5 


13 


3S 


22 


6 


5 


37 


25 


3 


30 


54 


21 


4 


22 


66 


32 


5 


14 


43 


25 


6 


6 


59 


40 


3 


31 


41 


16 


4 


23 


39 


19 


5 


15 


24 


14 


6 


7 


25 


17 


3 


32 


28 


11 


4 


24 


47 


23 


5 


16 


41 


24 


6 


8 


66 


45 


3 


33 


38 


15 


4 


25 


53 


26 


5 


17 


46 


27 


6 


9 


41 


28 


3 


34 


53 


21 


4 


26 


53 


26 


5 


18 


34 


20 


6 


10 


54 


37 


3 


35 


53 


21 


4 


27 


53 


26 


5 


19 


66 


39 


6 


11 


51 


35 


3 


36 


30 


12 


4 


28 


54 


27 


5 


20 


54 


32 


6 


12 


58 


40 


3 


37 


57 


23 


4 


29 


54 


27 


5 


21 


37 


2° 


6 


13 


42 


29 


3 


38 


57 


23 


4 


30 


54 


27 


5 


22 


62 


37 


6 


14 


39 


27 


3 


39 


37 


15 


4 


31 


199 


100 


5 


23 


62 


37 


6 


15 


59 


41 


3 


40 


54 


22 


4 


32 


137 


69 


5 


24 


30 


18 


6 


16 


66 


46 


3 


41 


66 


27 


4 


33 


89 


45 


5 


25 


30 


18 


6 


17 


53 


37 


3 


42 


51 


21 


4 


34 


67 


34 


5 


26 


53 


32 


6 


18 


30 


21 


3 


43 


46 


19 


4 


35 


53 


27 


5 


27 


38 


23 


6 


19 


57 


40 


3 


44 


41 


17 


4 


36 


47 


24 


5 


28 


28 


17 


6 


20 


54 


38 


3 


45 


24 


10 


4 


37 


39 


20 


5 


29 


41 


25 


6 


21 


34 


24 


3 


46 


43 


18 


4 


38 


66 


34 


5 


30 


54 


33 


6 


22 


41 


29 


3 


47 


57 


24 


4 


39 


62 


32 


5 


31 


62 


38 


6 


23 


62 


44 


3 


48 


57 


24 


4 


40 


54 


28 





32 


39 


24 


6 


24 


38 


27 


3 


49 


66 


28 


4 


41 


25 


13 


5 


33 


47 


29 


6 


25 


66 


47 


3 


50 


54 


23 


4 


42 


46 


24 


5 


34 


42 


26 


6 


26 


28 


20 


3 


51 


49 


21 


4 


43 


42 


22 


5 


35 


58 


36 | 


6 


27 


53 


38 


3 


52 


51 


22 


4 


44 


57 


30 


5 


36 


53 


33 


6 


28 


39 


28 


3 


53 


51 


22 


4 


45 


53 


28 


5 


37 


24 


15 i 


6 


29 


25 


18 


3 


54 


30 


13 


4 


46 


34 


18 


5 


38 


24 


15 


6 


30 


54 


39 


3 


55 


62 


27 


4 


47 


47 


25 


5 


39 


43 


27 


6 


31 


58 


42 


3 


56 


62 


27 


4 


48 


30 


16 


5 


40 


54 


34 


6 


32 


62 


45 


3 


57 


41 


18 


4 


49 


43 


23 


5 


41 


38 


24 


6 


33 


66 


48 


3 


58 


59 


26 


4 


50 


54 


29 


5 


42 


30 


19 


6 


34 


37 


27 


3 


59 


43 


19 


4 


51 


39 


21 


5 


43 


66 


42 


6 


35 


41 


30 


4 





54 


24 


4 


52 


37 


20 


5 


44 


66 


42 j 


6 


36 


30 


22 


4 


1 


47 


21 


4 


53 


59 


32 


5 


45 


47 


30 1 


6 


37 


34 


25 


4 


2 


58 


26 


4 


54 


57 


31 


5 


46 


39 


25 


6 


38 


38 


28 


4 


3 


58 


26 


4 


55 


66 


36 


5 


47 


42 


27 


6 


39 


46 


34 


4 


4 


62 


28 


4 


56 


62 


34 


5 


48 


59 


38 


6 


40 


54 


40 


4 


5 


66 


30 


4 


57 


58 


32 


5 


49 


34 


22 j 


6 


41 


66 


49 


4 


6 


57 


26 


4 


58 


58 


32 


5 


50 


54 


35 ! 


6 


42 


47 


35 


4 


7 


59 


27 


4 


59 


47 


26 


5 


51 


54 


35 


6 


43 


59 


44 


4 


8 


37 


17 


5 


0. 


54 


30 


5 


52 


46 


30 


6 


44 


28 


21 


4 


9 


39 


18 


5 


1 


43 


24 


5 


53 


49 


32 


6 


45 


28 


21 


4 


10 


54 


25 


5 


2 


59 


33 


5 


54 


58 


38 


6 


46 


28 


21 


4 


11 


43 


20 


5 


3 


41 


23 


5 


55 


38 


25 


6 


47 


57 


43 


4 


12 


30 


14 


5 


4 


41 


23 


5 


56 


47 


31 


6 


48 


49 


37 


4 


13 


47 


22 


5 


5 


62 


35 


5 


57 


59 


39 


6 


49 


66 


50 


4 


14 


34 


16 


5 


6 


30 


17 


5 


58 


59 


39 


6 


50 


54 


41 


4 


15 


53 


25 


5 


7 


51 


29 


5 


59 


54 


36 


6 


51 


46 


35 


4 


16 


57 


27 


5 


8 


28 


16 


6 





54 


36 


6 


52 


38 


29 


4 


17 


42 


20 


5 


9 


28 


16 


6 


1 


54 


36 


6 


53 


51 


39 


4 


18 


46 


22 


5 


10 


54 


31 


6 


2 


58 


39 


6 


54 


30 


23 


4 


19 


25 


12 


5 


11 


66 


38 


6 


3 


58 


39 


6 


55 


39 


30 


4 


20 


54 


26 


5 


12 


57 


33 


6 


4 


46 


31 


6 


56 


39 


30 



A Treatise on Milling and Milling Machines 363 



Table for Angular Indexing on the Universal Dividing Head 



s 

cd 


■ 
s 

3 


JD 


cd 


cd 
a> 


a 

CD 

3 


jo 


cd 


CO 

s 

CD 
U 


CO 
CD 

3 


JH 


CD 


co 

CD 
CD 

E 


CO 
CD 

■+* 
3 


o 


CD 


bO 
cd 

Q 


9 


*c3 
u 

b 


co 


bO 
CD 

P 


a 


fa 

5 


e3 

co 


5o 

CD 

Q 


9 


'6 


c3 
GO 


CD 

Q 


.9 


o 


aJ 

a 

CO 


6 


57 


57 


44 


7 


28 


47 


39 


7 


59 


62 


55 


8 


30 


54 


51 


6 


58 


62 


48 


7 


29 


47 


39 


8 





54 


48 


8 


31 


57 


54 


6 


59 


58 


45 


7 


30 


54 


45 


8 


1 


46 


41 


8 


32 


58 


55 


7 





54 


42 


7 


31 


43 


36 


8 


2 


28 


25 


8 


33 


59 


56 


7 


1 


59 


46 


7 


32 


13 


36 


8 


3 


38 


34 


8 


34 


62 


59 


7 


2 


59 


46 


7 


33 


62 


52 


8 


4 


58 


52 


8 


35 


43 


41 


7 


3 


37 


29 


7 


34 


25 


21 


8 


5 


59 


53 


8 


36 


66 


63 


7 


4 


28 


22 


7 


35 


38 


32 


8 


6 


30 


27 


8 


37 


47 


45 


7 


5 


47 


37 


7 


36 


58 


49 


8 


7 


51 


46 


8 


38 


49 


47 


7 


6 


38 


30 


7 


37 


39 


33 


8 


8 


62 


56 


8 


39 


51 


49 


7 


7 


43 


34 


7 


38 


66 


56 


8 


9 


53 


48 


8 


40 


54 


52 


7 


8 


53 


42 


7 


39 


66 


56 


8 


10 


54 


49 


8 


41 


28 


27 


7 


9 


34 


27 


7 


40 


54 


46 


8 


11 


66 


60 


8 


42 


30 


29 


7 


10 


54 


43 


7 


41 


41 


35 


8 


12 


34 


31 


8 


43 


62 


60 


7 


11 


30 


24 


7 


42 


62 


53 


8 


13 


46 


42 


8 


44 


34 


33 


7 


12 


30 


24 


7 


43 


42 


36 


8 


14 


47 


43 


8 


45 


37 


36 


7 


13 


51 


41 


7 


44 


57 


49 


8 


15 


24 


22 


8 


46 


39 


38 


7 


14 


51 


41 


7 


45 


43 


37 


8 


16 


49 


45 


8 


47 


42 


41 


7 


15 


41 


23 


7 


46 


51 


44 


8 


17 


38 


35 


8 


48 


46 


45 


7 


16 


57 


46 


7 


47 


37 


32 


8 


18 


51 


47 


8 


49 


49 


48 


7 


17 


42 


34 


7 


48 


30 


26 


8 


19 


66 


61 


8 


50 


54 


53 


7 


18 


37 


30 


7 


49 


38 


33 


8 


20 


54 


50 


8 


51 


59 


58 


7 


19 


59 


48 


7 


50 


54 


47 


8 


21 


57 


53 


8 


52 


66 


65 


7 


20 


54 


44 


7 


51 


47 


41 


8 


22 


43 


40 


8 


53 






7 


21 


49 


40 


7 


52 


24 


21 


8 


23 


58 


54 


8 


54 






7 


22 


66 


54 


7 


53 


24 


21 


8 


24 


30 


28 


8 


55 






7 


23 


39 


32 


7 


54 


49 


43 


8 


25 


62 


58 


8 


56 






7 


24 


62 


51 


7 


55 


58 


51 


8 


26 


47 


44 


8 


57 






7 


25 


57 


47 


7 


56 


59 


52 


8 


27 


49 


46 


8 


58 






7 


26 


46 


38 


7 


57 


43 


38 


8 


28 


34 


32 


8 


59 






7 


27 


58 


4S 


7 


58 


43 


38 


8 


29 


53 


50 


9 





1 Turn 



The angles given above are accurate to within one-half a minute 
with the exception of those printed in heavy faced type, in which 
the error is somewhat greater and may amount to a minute and in 
in some cases, slightly more. 



364 The Cincinnati Milling Machine Company 



CHAPTER XIX 
CHANGE GEARS FOR CUTTING SPIRALS 

We have seen in the chapter on spiral gears how the lead of the 
spiral is calculated. We shall now see how the machine is arranged 
to produce a given lead. 

The wormwheel in the Universal Dividing Head has 40 teeth 
and the worm is single threaded, therefore, 40 revolutions of the 
worm are required to make one revolution of the dividing head 
spindle. The table screw is so geared to the segment that the first 
change gear on this segment starting from the screw end makes 
one revolution for 34 " table movement. 

If equal change gears were used the wormshaft would also make 
one revolution for each x /±' table travel, and as the worm has 40 
teeth, the table would have to move 40 x M" = 10" for one full 
turn of the wormwheel and, therefore, for one turn of the spindle 
of the dividing head. In other words, a spiral of 10" lead will be 
produced if we use even change gears. If we want less lead we must 
speed up the wormshaft, and for more lead we must slow it down. 
This we do by means of the change gears furnished with the driv- 
ing mechanism of the dividing head. 

If the lead is to be one-third of 10" then we must speed up 3 to 1, 
and if the lead were three times 10", then we would slow down one- 
third of the speed of the first change gear. 

The Lead Divided by Ten is the Change Gear Ratio. For 

instance, to cut a spiral with a lead of 103^", divide 10^ by 10. 
Writing this as a common fraction we find that the change gear 

ratio is — — = , or — . We would get this result by placing a 

10 100 20 

20-tooth pinion on the first segment stud and a 21-tooth gear on 
the wormshaft. As these gears would be too far apart we would 
place two equal idlers somewhere between the two gears so as to 
connect them. However, looking up our list of change gears we find 
that we have neither a 20 nor a 21-tooth gear. Nor do we have mul- 
tiples of both. It is true we have a 40-tooth gear which is 2 times 20, 



A Treatise on Milling and Milling Machines 365 

but we have no gear with 2 times 21 teeth. We must therefore try 
to select our gears in such a way that we can compound them. 

21 

This we do by splitting the fraction into two other fractions 

20 

whose product equals the original fraction. This might be done in 

21 7x3 
different ways; for instance. = — . We might now look for 

20 4x5 

a pair of gears with a ratio of 7 to 4 and another pair with a ratio 
of 3 to 5; but, as we would like to have the gears as nearly of even 
size as we can get them, we multiply the numerator of the second 
fraction and the denominator of the first each by 2, which, of course, 

7x6 
does not change the value of the product. We then get . Mul- 

8x5 

tiplying both numerator and denominator of a fraction does not 
change its value. We may, therefore, make such a multiplication 
to raise the figures composing these fractions so they will correspond 
to the number of teeth in standard change gears furnished with the 

,..,.,,_ 7 8 56 , 6 8 48 
dividing head. Ihus — x — = - - and - - x - = — . 

8 8 64 5 8 40 

56 x 48 

The original ratio is not changed in value when written '■"—. 

64 x 40 

We saw above that if we had a 20 and a 21-tooth gear we could 
have placed the 21-tooth gear on the wormshaft and the 20-tooth 
on the first segment stud (called in the tables, gear for screw) and 
with two equal toothed idlers between to fill the space (which would 
not have affected the ratio) we could have proceeded to mill our 
spiral of 10 J^" lead. In this case the 20-tooth gear would have been 
the driver and the 21-tooth the driven gear. In the case of our 
compound gears, therefore, 64 and 40 are the drivers and 56 and 48 
are the driven gears. 

We place 64 on the first segment stud (gear for screw) and let it 
drive 56 (2d intermediate) and 48 on the wormshaft and drive it 
by 40 (1st intermediate), all as shown in Fig. 311. From this 
example the following rules may be deduced. 



366 The Cincinnati Milling Machine Company 

1st. = Change gear ratio, that is 

Lead Driven gears 
10 Driving gears 

2d. Resolve this fraction into two fractions. 

3d. Multiply the numerator and denominator of each fraction 
by some number (not necessarily the same number for both frac- 
tions) so as to get numbers corresponding to the number of teeth in 
standard change gears furnished with the machine. These numbers 
will then represent 

driven gears 2d interm. x gear on wormshaft __ lead 
driving gears 1st interm. x gear for screw 10 

lead 



Application of Continued Fractions. The fraction 



10 



is not always by any means as simple a fraction as the ones used in 
the preceding cases to illustrate the principle involved in com- 
puting change gears. Suppose, for example, it is desired to determine 
the proper change gears for a lead of 9.643". Our fraction now is 

— . Multiplying this by 1000 to get rid of the decimal, we have 

the fraction . Proceeding now as in the last example given 

10000 

in Chapter XVIII on Continued Fractions, we get the following: 



9643) IOOO0 (l 
9643 ; 
3 57)9643(27 
714 
2503 
2499 , 

4)357(89 
32 
37 
36 
1)4(4- 
± 
O 



A Treatise on Milling and Milling Machines 367 

Omitting the last two quotients and placing the others in our 
diagram as before, we get 

27 



1 27 



28 



27 
and our approximately equivalent fraction is, therefore, . Before 

we proceed further let us prove the accuracy of this fraction. We 
find by dividing 27 by 28 we get . 96425. We must remember that 

If* ?id 
our original fraction was - — , the value of which of course is one- 

10 

tenth the lead. That is approximately what we get when we divide 
27 by 28, as above. We must, therefore, multiply this result by 
ten in order to compare it with the original figure representing the 
lead. This gives us 9.6425, which subtracted from the actual lead, 
9 . 643, shows a difference of . 0005, entirely too small an amount to 
give us any concern. We may, therefore, proceed to split up our 

27 
fraction — so as to reduce it into fractions representing suitable 

change gears. Thus 

27 __ 3x9 

28 ~ 4 x 7 

3 16 48 9 8 72 
— X = — and — x — = 

4 16 64 7 8 56 

48 x 72 
We therefore have - J in which 48 and 72 are the driven gears 

64 x 56 

and 56 and 64 are the driving gears. We therefore proceed to place 
these on the machine as shown in Fig. 311, placing the 48-tooth 
gear on the second intermediate stud, the 72-tooth gear on the 
worm shaft, the 64-tooth gear on the first intermediate stud and the 
56-tooth gear on the stud in the segment next to and running at the 
same speed as the screw. 

In this connection it should be noted that it is permissible to 
transpose the 48-tooth gear and the 72-tooth gear and also the 56- 
tooth gear and the 64-tooth gear. This may make a more convenient 
combination to set up and does not affect the result at all. 



368 



The Cincinnati Milling Machine Company 



Fig. 311 shows the Divid- 
ing Head as used on a High- 
Power Universal Miller, 
geared up for a right-hand 
spiral, 10^" lead. 

We make a variety of 
machines and spiral cutting 
heads, and since the use of 
the idler varies with different 
combinations of spiral heads 
and machines, the following 
tabulation will prove of 
assistance.* 




Fig. 311 





No. 1 and No. 2 Cone-Driven 
Machines 


All High-Power Design 
Machines 




Right-Hand 
Spiral 


Left-Hand 

Spiral 


Right-Hand 
Spiral 


Left-Hand 

Spiral 


Dividing 
Head 


Do not use Idler 


Use Idler 


Use Idler 


Do not use Idler 


12" or 16" 

Spir. Head 


Use Idler 


Do not use Idler 


Do not use Idler 


Use Idler 



The table of leads on pages 338 and 339 gives a selected number 
of leads with corresponding combinations of change gears, angles, 
etc., for spirals up to 6" diameter and angles up to 45°. 

The table on pages 340 to 344 gives a complete list of leads up 
to 80", that can be obtained with the change gears regularly sup- 
plied without interference when they are placed on the machine. 
This will be found of great convenience, as the proper combination 
for almost any desired spiral can be taken from this table. 

For example: We want the proper gearing for a spiral of 21.1" 
lead. Consulting the table we find a lead of 21.116", and since this 
is only .016" longer than the theoretically correct lead, this gear 
combination can be used for all ordinary work. 

* Always withdraw the index plate stop before starting to cut spirals, 
because the index plate must be free to revolve with the index pointer. After 
the head has been geared up the table should always be moved by hand to 
insure that all parts are free to move, before throwing in the power feed. The 
Dividing Head should be placed in that slot of the table which is directly over 
the lead screw. 



A Treatise on Milling and Milling Machines 369 



Leads, Change Gears and Angles for Milling 

Twist Drills 

These tables are used in connection with standard cutters for 
milling twist drills. 



Diameter 

of 

Drill 


Pitch 

in 
Inches 


Gear 

on 
Worm 


1st Inter- 
mediate 
Gear 


2d Inter- 
mediate 
Gear 


Gear 
for 

Screw 


Angle 

of 
Spiral 


3 
16 


1.67 


24 


64 


32 


72 


19° 27' 


Vi 


1.94 


28 


64 


32 


72 


21° 


5 
16 


2.92 


28 


64 


48 


72 


20° 


H 


3.24 


28 


48 


40 


72 


21° 


7 
16 


3.89 


32 


64 


56 


72 


20° 10' 


l A 


4.17 


40 


64 


48 


72 


20° 30' 


9 
16 


4.86 


40 


64 


56 


72 


20° 


% 


5.33 


32 


40 


48 


72 


20° 12' 


11 
16 


6.12 


56 


40 


28 


64 


19° 30' 


H 


6.48 


40 


48 


56 


72 


20° 


13 
16 


7.29 


56 


64 


40 


48 


19° 20' 


Vs 


7.62 


48 


56 


64 


72 


19° 50' 


15 

16 


8.33 


48 


32 


40 


72 


19° 30' 


1 


8.95 


86 


56 


28 


48 


19° 20' 


V/% 


9.33 


48 


40 


56 


72 


20° 40' 



Twist drills are milled with the center part increasing in thick- 
ness toward the shank end. For different size drills this thickness 
varies as shown in table below. 

34" drill is -g±" thick at the point, and ^2" thick in the back. 

3^" drill is ye" thick at the point, and ^2" thick in the back. 

%" drill is -£2" thick at the point, and ye" thick in the back. 
1" drill is ^" thick at the point, and }/i" thick in the back. 
13^" drill is Y%" thick at the point, and £2" thick in the back. 

Other size drills vary in about the same proportion. 



d I u 



The Cincinnati Milling Machine Company 



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372 



The Cincinnati Milling Machine Company 



Leads from .670" to 3.143' 

Lead Driven 2d x Worm 



10 



Drivers 1st x Screw 



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© 


.670 


24 


86 


24 


100 


1.714 


40 


56 


24 


100 


2.442 


64 


48 


$<3 


.781 


24 


86 


2s 


100 


1.744 


24 


64 


40 


86 


2.444 


40 


72 


44 


100 


.soo 


24 


72 


24 


100 


1.750 


2S 


64 


40 100 


2.450 


56 


64 


2S 


100 


.893 


24 


86 


32 


100 


1.77S 


32 


72 


40 100 


2.456 


44 


86 


48 


100 


.900 


24 


64 


24 


100 


1.786 


32 


86 


4S 100 


2.481 


32 


72 


4S 


86 


.930 


24 


72 


24 


86 


1.809 


2s 


72 


40 I 86 


2.4S9 


32 


100 


56 


72 


.933 


24 


72 


2S 


100 


1.823 


2^ 


100 


56 | 86 


2.500 


24 


64 


48 


72 


1.029 


24 


56 


24 


100 


1.860 


24 


72 


48 ! 86 


2.514 


44 


56 


32 100 


1.042 


2S 


86 


32 


100 


1.867 


2S 


72 


48 100 


2.532 


2S 


72 


56 


86 


1.047 


24 


64 


24 


S6 


1.886 


44 


56 


24 100 


2.537 


24 


44 


40 


S6 


1.050 


24 


64 


2S 


100 


1.919 


24 


64 


44 86 


2.558 


32 


64 


44 


S6 


1.067 


2-1 


72 


32 


100 


1.925 


2S 


64 


44 100 


2.567 


44 


48 


2S 


100 


1 . 0S5 


24 


72 


2S 


86 


1.944 


28 


64 


32 72 


2.605 


28 


40 


32 1 86 


1.116 


24 


S6 


40 


100 


1.956 


32 


72 


44 100 


1 2.619 


24 


56 


44 72 


1.196 


24 


56 


24 


86 ! 


1.990 


28 


72 


44 86 


2.658 


32 


56 


40 86 


1.200 


24 


64 


32 


100 


1.993 


24 


56 


40 86 


2.667 


40 


72 


4S 100 


1.221 


24 


64 


2S 


S6 


2.000 


32 


64 


40 100 


2.674 


28 


64 


44 72 


1.228 


24 


86 


44 


100 


2.030 


24 


44 


32 S6 


2.713 


28 


48 


40 1 86 


1.240 


24 


72 


32 


86 


2.035 


28 


61 


40 86 


2.743 


48 


56 


32 100 


1.244 


2S 


72 


32 


100 


2.047 


40 


86 


44 100 


2.750 


40 


64 


44 100 


1.302 


2S 


86 


40 


100 


2.057 


48 


56 


24 100 


2.778 


32 


64 


40 72 


1.333 


24 


72 


40 


100 


2.067 


32 


72 


40 86 


2.791 


32 


64 


4S S6 


1 . 340 


24 


86 


4S 


100 


2. 083 


24 


64 


40 72 


2.800 


56 


64 


32 100 


1.371 


32 


56 


24 


100 


2.093 


24 


64 


48 86 


2.842 


40 


72 


44 86 


1.395 


24 


64 


32 


86 


2.100 


28 


64 


48 100 


2.849 


2S 


64 


56 $6 


1.400 


2S 


64 


32 


100 


2.133 


32 


72 


48 ilOO 


2.857 


24 


56 


48 72 


1.433 


2^ 


86 


44 


100 


2.171 


28 


72 


4S 86 


2.865 


44 


100 


56 86 


1.447 


2S 


72 


32 


86 


2.178 


28 


100 


56 


72 


2.880 


48 


40 


24 100 


1.45S 


24 


64 


2S 


72 


2.182 


40 


44 


24 


100 


2.894 


32 


72 


56 


S6 


1.467 


24 


72 


44 


100 


2.193 


24 


56 


44 86 


2.917 


2S 


64 


4S 


72 


1.488 


32 


86 


40 


100 


2.200 


32 


64 


44 100 


2.924 


32 


56 


44 


S6 


1.500 


40 


64 


24 


100 


2 . 222 


28 


56 


32 72 


2.933 


44 


72 


48 100 


1.550 


24 


72 


40 


86 


2.233 


40 


86 


48 100 


2.946 


44 


56 


24 


64 


1.556 


28 


72 


40 


100 


2.238 


28 


64 


44 86 


2.960 


2S 


44 


40 


86 


1.563 


2S 


86 


4S 


100 


2.274 


32 


72 


44 


86 


2.984 


28 


48 


44 


86 


1.595 


24 


56 


32 


86 


2.286 


32 


56 


40 


100 


3.000 


40 


64 


48 


100 


1.600 


24 


72 


4S 


100 


2.292 


24 


64 


44 


72 


3.044 


24 


44 


4S 


86 


1.628 


28 


64 


32 


86 


2^326 


32 


64 


40 


86 


3.056 


32 


64 


44 


72 


1.637 


32 


S6 


44 


100 


2.368 


28 


44 


32 


86 


3.070 


24 


40 


44 


86 


1.650 


44 


64 


24 


100 


2.381 


24 


56 


40 


72 


3.101 


40 


72 


48 


86 


1.667 


24 


64 


32 


72 


2.392 


24 


56 


48 86 


3.111 


40 


100 


56 


72 


1.705 


24 


72 


44 


86 


2.400 


32 


64 


4n 100 


3.126 


4S 


100 


56 


86 


1.711 


2S 


72 


44 


100 


2.431 


28 


64 


40 72 


3.143 


40 


56 


44 100 



A Treatise on Milling and Milling Machines 373 



Leads from 3.175* to 6.667" 

Driven 2d x Worm 



Lead 
~I6~ 



Drivers 1st x Screw 



a> 










W 










w 










03 










S 










03 










-a 




Fh 


>-, 




,4 




Fh 


Fh 




Xi 




Fh 


Fh 




a 




93 


c3 




o 




d 


oj 




o 




c3 


c3 




a 
i—i 




03 

o 


03 

o 




a 

1— 1 




03 

o 


03 

o 




a 




03 

o 


03 

o 




a 




2 


03 




a 




03 


03 




( d 




03 


03 




_ 


S 


5 


c3 


£ 


^-, 


S 


s 


•+3 

o3 


* 


_i 


S 


5 


+3 

o3 


* 


c3 
u 

'a, 

02 




-3 
S 03 


<u a 


0) 

02 <3 

Fh > 


o3 

a 

02 


Fh 


■3 

S 03 


cu a 


03 
Fh 

02 5 


c3 
Fh 

ft 

02 


Fh 


-3 

03'—. 

S 03 
Fh > 


03 a 


03 

Fh 

02 03 

Fh > 


o 

o3 


c3^ 


i— i -3- 




«2" c 
Q 

o3^ 


o 

o3 


o3 ^ 


03 •{-! 


03 'C 

i— i — ' 


«2' c 
Q 

c3^ 


o 

o3 


o3 w 


03 -rl 
t— 1 o 


03 *C 

I— i ^—' 


o 'C 


03 


03 

o 


03 

i— 1 


T3 


a 


0) 


03 

O 


03 
i—l 


T3 


03 

o 


03 
*1 


03 

o 


to 

1— 1 




03 

o 


3.175 


32 


56 


40 


72 


4.040 


32 


44 


40 


72 


5.185 


32 


48 


56 


72 


3.189 


32 


56 


48 


86 


4.059 


32 


44 


48 


86 


5.209 


56 


40 


32 


86 


3.198 


40 


64 


44 


86 


4.070 


40 


64 


56 


86 


5.226 


86 


64 


28 


72 


3.241 


28 


48 


40 


72 


4.074 


32 


48 


44 


72 


5.238 


44 


56 


48 


72 


3.256 


32 


64 


56 


86 


4.093 


32 


40 


44 


86 


5.316 


40 


56 


64 


86 


3.267 


56 


48 


28 


100 


4.134 


40 


72 


64 


86 


5.333 


32 


40 


48 


72 


3.300 


44 


64 


48 


100 


4.144 


56 


44 


28 


86 


5.347 


44 


64 


56 


72 


3.307 


32 


72 


64 


86 


4.167 


40 


64 


48 


72 


5.357 


48 


64 


40 


56 


3.333 


32 


64 


48 


72 


4.200 


48 


100 


56 


64 


5.412 


64 


44 


32 


86 


3.349 


24 


40 


48 


86 


4.242 


28 


44 


48 


72 


5.426 


40 


48 


56 


86 


3.360 


48 


40 


28 


100 


4.252 


32 


56 


64 


86 


5.444 


56 


40 


28 


72 


3.383 


32 


44 


40 


86 


4.264 


40 


48 


44 


86 


5.568 


56 


44 


28 


64 


3.403 


28 


64 


56 


72 


4.286 


48 


64 


32 


56 


5.625 


72 


48 


24 


64 


3.411 


44 


72 


48 


86 


4.341 


48 


72 


56 


86 


5.657 


32 


44 


56 


72 


3.422 


44 


100 


56 


72 


4.364 


48 


44 


40 


100 


5.714 


64 


48 


24 


56 


3.429 


40 


56 


48 


100 


4.365 


40 


56 


44 


72 


5.759 


86 


56 


24 


64 


3.488 


40 


64 


48 


86 


4.375 


56 


48 


24 


64 


5.788 


56 


72 


64 


86 


3.492 


32 


56 


44 


72 


4.385 


44 


56 


48 


86 


5.833 


48 


64 


56 


72 


3.500 


40 


100 


56 


64 


4.444 


28 


56 


64 


72 


5.847 


44 


56 


64 


86 


3.520 


44 


40 


32 


100 


4.465 


32 


40 


48 


86 


5.893 


48 


64 


44 


56 


3.552 


28 


44 


48 


86 


4.477 


44 


64 


56 


86 


5.920 


40 


44 


56 


86 


3.565 


28 


48 


44 


72 


4.480 


56 


40 


32 


100 


5.926 


64 


48 


32 


72 


3.581 


28 


40 


44 


86 


4.537 


28 


48 


56 


72 


5.954 


64 


40 


32 


86 


3.618 


40 


72 


56 


86 


4.548 


44 


72 


64 


86 


5.969 


44 


48 


56 


86 


3.636 


24 


44 


48 


72 


4.558 


56 


40 


28 


86 


5.972 


86 


48 


24 


72 


3.654 


40 


56 


44 


86 


4.583 


44 


64 


48 


72 


6.061 


40 


44 


48 


72 


3.667 


44 


48 


40 


100 


4.667 


28 


40 


48 


72 


6.109 


56 


44 


48 


100 


3.704 


32 


48 


40 


72 


4.736 


32 


44 


56 


86 


6.125 


56 


40 


28 


64 


3.721 


28 


56 


64 


86 


4.762 


40 


56 


48 


72 


6.136 


72 


44 


24 


64 


3.733 


48 


100 


56 


72 


4.773 


56 


44 


24 


64 


6.140 


44 


40 


48 


86 


3.750 


48 


64 


28 


56 


4.821 


72 


56 


24 


64 


6.160 


56 


40 


44 


100 


3.771 


44 


56 


48 


100 


4.848 


32 


44 


48 


72 


6.202 


40 


48 


64 


86 


3.798 


28 


48 


56 


86 


4.861 


40 


64 


56 


72 


6.222 


64 


40 


28 


72 


3.810 


32 


56 


48 


72 


4.884 


48 


64 


56 


86 


6.234 


64 


44 


24 


56 


3.819 


40 


64 


44 


72 


4.889 


32 


40 


44 


72 


6.349 


40 


56 


64 


72 


3.837 


44 


64 


48 


86 


4.949 


56 


44 


28 


72 


6.364 


56 


44 


32 


64 


3.840 


48 


40 


32 


100 


4.961 


48 


72 


64 


86 


6.379 


48 


56 


64 


86 


3.850 


44 [100 


56 


64 


5.074 


40 


44 


48 


86 


6.429 


72 


56 


32 


64 


3.889 


32 


64 


56 


72 


5.080 


32 


56 


64 


72 


6.465 


64 


44 


32 


72 


3.907 


28 


40 


48 


86 


5.093 


40 


48 


44 


72 


6.481 


40 


48 


56 


72 


3.920 


56 


40 


28 


100 


5.104 


56 


48 


28 


64 


6.515 


86 


44 


24 


72 


3.979 


44 


72 


56 


86 


5.119 


86 


56 


24 


72 


6.563 


72 


48 


28 


64 


3.986 


40 


56 


48 


86 


i 5.133 


56 


48 


44 


100 


6.667 


64 


56 


28 


48 



374 



The Cincinnati Milling Machine Company 



Leads from 6.720'' to 12.444" 

Lead Driven 2d x Worm 



10 



Drivers 1st x Screw 



Inches 




f-i 
o3 
0) 

O 


F-i 

03 
CD 

o 




Inches 




F-i 
03 
CD 

o 


pi 

o3 

o 




CO 
CD 

o 

CI 




F-i 
o3 
CD 

o 


F-i 

03 

CD 
O 




.9 

F-i 
"ft 

GO 


S 

Eh 


CD 




F-i _^ 

u > 


'ft 

m 


S 

F-i 


CD 

a a; 
£ > 


CD 

H-> 

o3 

CD d 
g£ 


CD 

Ul CD 

u > 


F-I 

w. 


_ > 


CD 
-*> 
03 

CD<"^ 

S v 


CD 
o3 

cd a 
g> 


is 

F-l _ 

'f7 
GO CD 

F-, > 


O 

-d 

o3 


§ P 

o3^ 


CD •'-' 

dp 


"SO 

l—l v — ' 


t2' E 
P 

o3 


o 

nd 

c3 


o3^ 


a, .-J 


CD 'S 


«2'S 

P 
f-> & 

o3^ 


O 

o3 


o3 w 


CD •£ 

«P 


CD 'fl 

"SP 

r- 1 s -^' 


P 

o3^ 


CD 
►H 


CD 

o 


m 


-d 

CM 


CD 

o 


CD 


CD 

o 


+3 

02 

rH 


T3 


CD 

o 


CD 
rH 


CD 

o 


m. 

rH 


73 
CM 


CD 

o 


6.720 


56 


40 


48 


100 


8.212 


86 


64 


44 


72 


10.238 


86 


56 


48 


72 


6.750 


72 


40 


24 


64 


8.250 


48 


64 


44 


40 


10.286 


72 


40 


32 


56 


6.765 


40 


44 


64 


86 


8.312 


64 


56 


32 


44 


10.313 


72 


64 


44 


48 


6.806 


56 


32 


28 


72 


8.333 


48 


32 


40 


72 


10.370 


56 


48 


64 


72 


6.822 


44 


48 


64 


86 


8.361 


86 


40 


28 


72 


10.390 


64 


56 


40 


44 


6.825 


86 


56 


32 


72 


8.377 


86 


44 


24 


56 


10.419 


56 


40 


64 


86 


6.968 


86 


48 


28 


72 


8.485 


48 


44 


56 


72 


10.451 


86 


64 


56 


72 


6.984 


44 


56 


64 


72 


8.532 


86 


56 


40 


72 


10.476 


64 


56 


44 


48 


7.000 


56 


40 


32 


64 


8.551 


86 


44 


28 


64 


10.500 


56 


64 


48 


40 


7.013 


72 


44 


24 


56 


8.555 


44 


40 


56 


72 


10.558 


86 


64 


44 


56 


7.071 


40 


44 


56 


72 


8.571 


72 


56 


32 


48 


10.667 


48 


40 


64 


72 


7.104 


48 


44 


56 


86 


8.682 


64 


48 


56 


86 


10.694 


56 


32 


44 


72 


7.111 


64 


40 


32 


72 


8.687 


86 


44 


32 


72 


10.714 


72 


56 


40 


48 


7.130 


44 


48 


56 


72 


8.839 


72 


64 


44 


56 


10.750 


86 


40 


32 


64 


7.159 


72 


44 


28 


64 


8.889 


56 


28 


32 


72 


10.859 


86 


44 


40 


72 


7.163 


44 


40 


56 


86 


8.930 


48 


40 


64 


86 


10.909 


72 


48 


32 


44 


7.167 


86 


40 


24 


72 


8.958 


86 


56 


28 


48 


10.938 


56 


32 


40 


64 


7.273 


64 


44 


28 


56 


9.000 


72 


40 


28 


56 


10.949 


86 


48 


44 


72 


7.292 


56 


64 


40 


48 


9.143 


64 


40 


32 


56 


11.111 


64 


32 


40 


72 


7.330 


86 


44 


24 


64 


9.166 


48 


32 


44 


72 


11.168 


86 


44 


32 


56 


7.333 


44 


40 


48 


72 


9.214 


86 


40 


24 


56 


11.163 


72 


48 


64 


86 


7.407 


40 


48 


64 


72 


9.333 


48 


40 


56 


72 


11.198 


86 


64 


40 


48 


7.465 


86 


64 


40 


72 


9.351 


72 


56 


32 


44 


11.250 


72 


32 


28 


56 


7.500 


72 


48 


32 


64 


9.375 


72 


64 


40 


48 


11.313 


56 


44 


64 


72 


7.601 


86 


44 


28 


72 


9.385 


86 


56 


44 


72 


11.402 


86 


44 


28 


48 


7.619 


48 


56 


64 


72 


9.406 


86 


40 


28 


64 


11.518 


86 


64 


48 


56 


7.679 


86 


64 


32 


56 


9.429 


48 


56 


44 


40 


11.667 


56 


32 


48 


72 


7.714 


72 


40 


24 


56 


9.471 


56 


44 


64 


86 


11.688 


72 


56 


40 


44 


7.778 


64 


32 


28 


72 


9.524 


64 


56 


40 


48 


11.758 


86 


32 


28 


64 


7.814 


48 


40 


56 


86 


9.545 


72 


48 


28 


44 


11.786 


72 


56 


44 


48 


7.839 


86 


48 


28 


64 


9.556 


86 


40 


32 


72 


11.852 


64 


24 


32 


72 


7.875 


72 


40 


28 


64 


9.568 


72 


56 


64 


86 


12.000 


72 


40 


32 


48 


7.955 


56 


64 


40 


44 


9.598 


86 


64 


40 


56 


12.031 


56 


32 


44 


64 


7.963 


86 


48 


32 


72 


9.625 


56 


64 


44 


40 


12.040 


86 


40 


56 


100 


8.000 


64 


40 


28 


56 


9.643 


72 


64 


48 


56 


12.121 


64 


48 


40 


44 


8.021 


56 


64 


44 


48 


9.697 


64 


48 


32 


44 


12.178 


72 


44 


64 


86 


8.036 


72 


64 


40 


56 


9.722 


56 


32 


40 


72 


12.216 


86 


64 


40 


44 


8.063 


86 


40 


24 


64 


9.773 


86 


44 


32 


64 


12.222 


48 


24 


44 


72. 


8.081 


40 


44 


64 


72 


9.778 


44 


40 


64 


72 


12.273 


72 


64 


48 


44 


8.118 


48 


44 


64 


86 


9.844 


72 


32 


28 


64 


12.286 


86 


40 


32 


56 


8.148 


44 


48 


64 


72 


9.954 


86 


48 


40 


72 


12.318 


86 


64 


44 


48 


8.182 


72 


44 


28 


56 


10.159 


64 


28 


32 


72 


12.375 


72 


40 


44 


64 


8.186 


44 


40 


64 


86 


10.227 


72 


64 


40 


44 


12.444 


56 


40 


64 


72 



A Treatise on Milling and Milling Machines 375 



Leads from 12.468" to 24.635" 

Driven 2d x Worm 



Lead 
^0~ 



Drivers 1st x Screw 



00 








1 


oo 






| 


00 










S 




(.« 


t* 




05 




u 


t_ 




05 




Lh 


d 




o 




a 


c3 




o 




03 


o3 




o 




c3 


a 




a 

t-H 




05 

o 


eg 

a 




h- 1 




05 

o 


05 

a 




d 

m 




05 

o 


05 

O 




.9 


B 


2 


05 


fe 


.s 


S 


05 
o3 


05 
•*> 


* 


>"3 


a 


05 

5 


05 
o3 


* 


a9 

"ft 

CO 




£ 05 


05 a 


05 

co & 

s- > 


c3 

ft 

GO 




05^ 
S 05 


•medi: 
ven) 


05 

S-c 

CO 05 

t* > 


as 

S-i 
"ft 

co 




-3 

S 05 


05 £ 

a > 


05 

° IT 

CO 05 
*- > 


o 

c3 


o3^ 




oj *n 
"SO 


3.'* 

Q 

** ti- 
es w 


<4H 

o 

e3 


*-> G- 


05 -C 

CD 
t— i O 


05 'C 

"SB 


e3^ 


tl-l 

o 

e3 


o3 w 


05 -jh 

1— 1 w 


«5 £ 

a C 
i— i 


,2" c 

Q 
f-> G- 

03 


h3 


a> 

O 


■4-3 

00 

i— 1 


T3 


05 

a 


05 

h3 


05 

o 


OQ 


-d 


05 

o 


05 


05 

o 


-*3 
00. 

i— 1 




05 

o 


12.468 


64 


56 


48 


44 


15.429 


72 


56 


48 


40 


19.196 


86 


32 


40 


56 


12.500 


56 


28 


40 


64 


15.469 


72 


32 


44 


64 


19.286 


72 


32 


48 


56 


12.542 


86 


40 


28 


48 


15.556 


64 


32 


56 


72 


19.592 


64 


28 


48 


56 


12.571 


64 


56 


44 


40 


15.636 


86 


40 


32 


44 


19.636 


72 


44 


48 


40 


12.698 


64 


28 


40 


72 


15.677 


86 


64 


56 


48 


19.688 


72 


32 


56 


64 


12.798 


86 


56 


40 


48 


15.714 


64 


32 


44 


56 


19.708 


86 


48 


44 


40 


12.833 


56 


48 


44 


40 


15.750 


72 


64 


56 


40 


19.907 


86 


24 


40 


72 


12.857 


72 


28 


32 


64 


15.926 


86 


48 


64 


72 


20.156 


86 


64 


72 


48 


12.963 


56 


24 


40 


72 


16.071 


72 


32 


40 


56 


20.204 


72 


28 


44 


56 


13.030 


86 


48 


32 


44 


16.125 


86 


64 


48 


40 


20.364 


64 


44 


56 


40 


13.091 


72 


40 


32 


44 


16.288 


86 


48 


40 


44 


20.455 


72 


32 


40 


44 


13.125 


56 


32 


48 


64 


16.296 


64 


24 


44 


72 


20.476 


86 


56 


64 


48 


13.139 


86 


40 


44 


72 


16.424 


86 


32 


44 


72 


20.571 


72 


56 


64 


40 


13.333 


64 


32 


48 


72 


16.500 


72 


48 


44 


40 


20.625 


72 


48 


44 


32 


13.395 


72 


40 


64 


86 


16.722 


86 


40 


56 


72 


20.741 


64 


24 


56 


72 


13.438 


86 


32 


28 


56 


16.753 


86 


56 


48 


44 


20.903 


86 


32 


56 


72 


13.500 


72 


64 


48 


40 


16.797 


86 


32 


40 


64 


20.952 


64 


24 


44 


56 


13.636 


72 


48 


40 


44 


16.875 


72 


32 


48 


64 


21.000 


72 


48 


56 


40 


13.651 


86 


28 


32 


72 


16.893 


86 


56 


44 


40 


21.116 


86 


32 


44 


56 


13.714 


64 


56 


48 


40 


16.970 


64 


48 


56 


44 


21.429 


72 


28 


40 


48 


13.750 


56 


28 


44 


64 


17.063 


86 


28 


40 


72 


21.818 


72 


48 


64 


44 


13.935 


86 


24 


28 


72 


17.102 


86 


64 


56 


44 


21.939 


86 


28 


40 


56 


13.961 


86 


56 


40 


44 


17.143 


72 


56 


64 


48 


21.989 


86 


64 


72 


44 


13.968 


64 


28 


44 


72 


17.277 


86 


64 


72 


56 


22.041 


72 


28 


48 


56 


14.026 


72 


56 


48 


44 


17.374 


86 


44 


64 


72 


22.338 


86 


56 


64 


44 


14.063 


72 


32 


40 


64 


17.455 


64 


44 


48 


40 


22.396 


86 


32 


40 


48 


14.077 


86 


56 


44 


48 


17.500 


56 


24 


48 


64 


22.500 


72 


28 


56 


64 


14.143 


72 


56 


44 


40 


17.551 


86 


28 


32 


56 


22.803 


86 


48 


56 


44 


14.259 


56 


24 


44 


72 


17.679 


72 


56 


44 


32 


22.857 


64 


24 


48 


56 


14.286 


64 


32 


40 


56 


17.777 


64 


28 


56 


72 


22.909 


72 


44 


56 


40 


14.318 


72 


64 


56 


44 


17.917 


86 


32 


48 


72 


23.036 


86 


56 


72 


48 


14.333 


86 


40 


48 


72 


17.959 


64 


28 


44 


56 


23.333 


64 


48 


56 


32 


14.659 


86 


64 


48 


44 


18.333 


64 


48 


44 


32 


23.455 


86 


44 


48 


40 


14.667 


64 


48 


44 


40 


18.367 


72 


28 


40 


56 


23.516 


86 


64 


56 


32 


14.694 


72 


28 


32 


56 


18.429 


86 


56 


48 


40 


23.571 


72 


28 


44 


48 


14.781 


86 


64 


44 


40 


18.477 


86 


32 


44 


64 


23.889 


86 


32 


64 


72 


14.815 


64 


24 


40 


72 


18.667 


64 


48 


56 


40 


24.000 


72 


48 


64 


40 


14.931 


86 


32 


40 


72 


18.701 


72 


56 


64 


44 


24.133 


86 


28 


44 


56 


15.000 


56 


28 


48 


64 


18.750 


72 


32 


40 


48 


24. 188 


86 


64 


72 


40 


15.202 


86 


44 


56 


72 


18.770 


86 


28 


44 


72 


24.432 


86 


32 


40 


44 


15.238 


64 


28 


48 


72 


18.813 


86 


64 


56 


40 


24.545 


72 


44 


48 


32 


15.273 


56 


44 


48 


40 


19.091 


72 


48 


56 


44 


24.571 


86 


56 


64 


40 


15.357 


86 


28 


32 


64 


19.111 


86 


40 


64 


72 


24.635 


86 


48 


44 


32 



376 



The Cincinnati Milling Machine Company 



Leads from 24.750" to 80.625" 

Lead Driven 2d x Worm 



10 



Drivers 1st x Screw 



CO 










CO 
CD 










CO 

CD 










rd 




Fh 


u 




-a 




Fh 


Fh 




43 




Fh 


Fh 




o 




03 


o3 




o 




o3 


o3 




o 




03 


o3 




d 
i— i 




CD 

o 


CD 

o 




d 
i—i 




CD 

o 


CD 

o 




d 
i—i 




CD 

a 


CD 

o 




.3 




cd 


CD 




.£ 




CD 


CD 




# d 




CD 






"e3 

Fh 

"ft 


Fh 


-*3 

£ > 


o3 

'So 

<u d 


<u 

Fh _ 

m £ 

u > 


'o3 

Fh 
'ft 


S 

Fh 


-t-3 

£ > 


03 

CD d 
d CD 


CD 

8-i 

°o 

W. CD 


"Si 

_Fh 
"ft 

m 


S 

Fh 


+3 

S3 

-3 

CD^ 
S CD 
F- > 


o3 

^O 
CD d 

g £ 


CD 

Fh 

m cd 

Fh > 


O 
o3 


*-> G 

o3^ 


cd t 1 

sQ 

h- 1 G 


a> "3 


«2' c 
t* G 

o3^ 


«+h 

O 

o3 


*-• G 

o3^ 


CD -jH 

■+* 22 

HH G 


CD *E 

dQ 

i—i ^— ' 


Q 

s- 1 G 

o3^ 


o 

o3 


*-> G 

03 


cd •rj 

■ +=> 22 

i— i G 


CD "fi 

"SO 
i— i v — ' 


.2" c 

Q 
f- G 

o3 




o 


GO 
i— 1 




cd 

o 


CD 
1-3 


CD 

o 


02 




CD 

o 


CD 


CD 

O 


CO 

1—1 


t3 


a> 

o 


24.750 


72 


40 


44 


32 


30.857 


72 


28 


48 


40 


40.952 


86 


28 


64 


48 


25.083 


86 


48 


56 


40 


31.111 


64 


24 


56 


48 


41.143 


72 


28 


64 


40 


25.130 


86 


56 


72 


44 


31.273 


86 


44 


64 


40 


41.806 


86 


24 


56 


48 


25.455 


64 


44 


56 


32 


31.354 


86 


48 


56 


32 


42.232 


86 


28 


44 


32 


25.595 


86 


28 


40 


48 


31.500 


72 


40 


56 


32 


43.000 


86 


40 


64 


32 


25.714 


72 


56 


64 


32 


31.852 


86 


24 


64 


72 


43.636 


72 


24 


64 


44 


26.061 


86 


48 


64 


44 


32.000 


64 


28 


56 


40 


43.977 


86 


44 


72 


32 


26.182 


72 


44 


64 


40 


32.250 


86 


48 


72 


40 


44.675 


86 


28 


64 


44 


26.250 


72 


48 


56 


32 


32.576 


86 


24 


40 


44 


45.000 


72 


28 


56 


32 


26.327 


86 


28 


48 


56 


32.727 


72 


44 


64 


32 


45.606 


86 


24 


56 


44 


26.667 


64 


28 


56 


48 


32.847 


86 


24 


44 


48 


46.071 


86 


28 


72 


48 


26.875 


86 


28 


56 


64 


33.507 


86 


28 


48 


44 


47.778 


86 


24 


64 


48 


27.000 


72 


40 


48 


32 


33.786 


86 


28 


44 


40 


48.000 


72 


24 


64 


40 


27.302 


86 


28 


64 


72 


33.939 


64 


24 


56 


44 


48.375 


86 


40 


72 


32 


27.364 


86 


44 


56 


40 


34.205 


86 


44 


56 


32 


49.143 


86 


28 


64 


40 


27.500 


72 


24 


44 


48 


34.286 


72 


28 


64 


48 


50.167 


86 


24 


56 


40 


27.643 


86 


56 


72 


40 


34.554 


86 


56 


72 


32 


50.260 


86 


28 


72 


44 


27.922 


86 


28 


40 


44 


35.000 


72 


24 


56 


48 


51.429 


72 


28 


64 


32 


28.000 


64 


40 


56 


32 


35.102 


86 


28 


64 


56 


52.121 


86 


24 


64 


44 


28.052 


72 


28 


48 


44 


35.182 


86 


44 


72 


40 


53.750 


86 


28 


56 


32 


28.155 


86 


28 


44 


48 


35.833 


86 


48 


64 


32 


55.286 


86 


28 


72 


40 


28.636 


72 


44 


56 


32 


36.000 


72 


40 


64 


32 


57.333 


86 


24 


64 


40 


28.667 


86 


48 


64 


40 


36.857 


86 


28 


48 


40 


58.636 


86 


24 


72 


44 


29.091 


64 


28 


56 


44 


37.403 


72 


28 


64 


44 


60.000 


72 


24 


64 


32 


29.318 


86 


48 


72 


44 


37.625 


86 


40 


56 


32 


61.429 


86 


28 


64 


32 


29.388 


72 


28 


64 


56 


38.182 


72 


24 


56 


44 


62.708 


86 


24 


56 


32 


29.563 


86 


40 


44 


32 


39.091 


86 


44 


64 


32 


64.500 


86 


24 


72 


40 


29.861 


86 


24 


40 


48 


39.417 


86 


24 


44 


40 


69.107 


86 


28 


72 


32 


30.000 


72 


48 


64 


32 


39.490 


86 


28 


72 


56 


71.667 


86 


24 


64 


32 


30.234 


86 


64 


72 


32 


40.000 


72 


24 


64 


48 


80.625 


86 


24 


72 


32 


30.714 


86 


56 


64 


32 


40.313 


86 


48 


72 | 32 













A Treatise on Milling and Milling Machines 377 



CHAPTER XX 
MILLING SPIRAL CAMS 

In this chapter we give detailed tables for setting Cincinnati 
Millers for Milling Screw Machine Cams and other spiral cams with 
leads between .600" and 6.00" advancing by .001". 

The cutting of accurate screw machine cams is one of the most 
difficult jobs that comes to the toolroom, because of the intricate 
computations necessary to determine the correct settings. Such 
cams are required in great variety, each differing from the other by 
only a few thousandths and with practically no duplications, making 
the use of master cams out of the question. These cams usually 
have shorter leads than can be obtained on a dividing head by any 
practical combination of change gears. It is therefore necessary to 




Fig. 312 

use a vertical attachment in connection with the dividing head and 
set both of them to that angle, which, together with the lead produced 
by the change gears, gives the correct lead to produce the required 
cam. 

It is the computation of these angular settings in connection 



378 The Cincinnati Milling Machine Company 

with the proper change gear combinations that involves mathe- 
matics which is sometimes too confusing for the toolmaker. 

In the tables following all the information is given, and it 
only remains for the milling machine operator to select the lead of 
the desired cam from the tables and set up to the corresponding 
change gears and angles. 

Example: To set the machine for a cam having .717" lead. 

Setting the Vertical Attachment. Read the angle direct from 
the dial and set the spindle 39^° from its vertical position. 

Setting the Dividing Head. Subtract the angle in the table 
from 90°. The difference represents the angle to which the spindle 
must be raised from the horizontal position. 

90° - 39J^° = 50^°. 

Set the dividing head spindle 503^ up from the horizontal 
position. This angle is read direct from the dial. 

Follow this same method when setting up for any other similar 
cams. 



A Treatise on Milling and Milling Machines 379 





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.650 


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86 


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100 


14 


.700 


24 


72 


24 


100 


29 


.601 ! 24 86 24 


100 


26 


.651 


24 


86 


28 


100 


33/2 


.701 


24 


72 


24 


86 


41 


.602, 24 1 86 24 


100 


26 


.652 


24 


86 


24 


100 


13/t 


.702 


24 


86 


28 


100 


26 


.603, 24! 86 


28 


100 


39 fe 


.653 


24 


66 


32 


100 


43 


.703 


24 


72 


24 


100 


28V2 


.604! 24 1 72 


24 


100 


41 


.654 


24 


86 


24 


100 


12 /z 


.704 


24 


86 


32 


100 


38 


.605] 24 


86 


24 


100 


25 Vi 


.655 


24 


86 


24 


100 


12 


.705 


24 


86 


28 


100 


25 Vz 


.606 24 


86 


28 


100 


39 


.656 


24 


86 


24 


100 


II Vi 


.706 


24 


72 


24 


100 


28 


.607 


24 


86 


24 


100 


25 


.657 


24 


86 


24 


100 


11 


.707 


24 


72 


24 


86 


40 V 2 


.608 


24 


72 


24 


100 


40'/2 


.658 


24 


86 


32 


too 


42*2 


.708 


24 


86 


28 


100 


25 


.609 


24 


86 


24 


100 


24/a 


.659 


24 


72 


24 


too 


34«/z 


.709 


24 


72 


28 


100 


40/2 


.610 


24 


66 


24 


100 


24 fc 


.660 


24 


86 


24 


100 


10 


.710 


24 


72 


24 


100 


27»/z 


.611 


24 


86 


28 


100 385ft 


.661 


24 


86 


28 


100 


32 


.711 


24 


86 


28 


100 


24/2 


.6ie 


24 


86 


24 


I00|24 


.662 


24 


86 


28 


100 


32 


.712 


24 


72 


24 


86 


40 


.613 


24 


72 


24 


100 40 


.663 


24 


72 


24 


too 


34 


.713 


24 


72 


24 


100 


27 


.614 


24 


86 


24 


100 


23/2 


.664 


24 


86 


32 


100 


42 


.714 


24 


64 


24 


100 


37/2 


.615 


24 


86 


28 


100 


38 


.665 


24 


72 


28 


100 


44/2 


.715 


24 


72 


28 


100 


40 


.616 


24 


86 


24 


100 


23 


.666 


24 


86 


28 


100 


31 '/2 


.716 


24 


86 


28 


100 


23 Vz 


.617 


24 


72 


24 


too 


39'/z 


.667 


24 


72 


24 


100 


33 Vz 


.717 


24 


72 


24 


86 


39'/« 


.618 


24 


72 


24 


100 


39'/ 2 


.668 


24 


64 


24 


100 


42 


.718 


24 


86 


32 


100 


36*2 


.619 


24 


86 


24 100 


22'/2 


.669 


24 


72 


24 


86 


44 


.719 


24 


86 


28 


100 


23 


.620 


24 


86 


28 100 


37'/2 


.670 


24 


86 


28 


100 


31 


.720 


24 


72 


28 


100 


39 % 


.621 


24 


86 


24 


100 


22 


.671 


24 


72 


24 


too 


33 


.721 


24 


86 


28 


100 


22/2 


.622 


24 


72 


24 


100 


39 


.672 


24 


86 


28 


100 


30/2 


.722 


24 


72 


24 


100 


25»/2 


.623 


24 


86 


24 


100 


21 '/2 


.673 


24 


86 


28 


loo 


30«/2 


.723 


24 


64 


24 


100 


36/2 


.624 


24 


86 


28 


100 


37 


,674 


24 


64 


24 


100 


41 & 


.724 


24 


86 


28 


100 


22 


.625 


24 


86 


24 


100 


21 


.675 


24 


72 


24 


100 


32»/2 


.725 


24 


72 


24 


100 


25 


.626 


24 


86 


32 


100 


45 Vz 


.676 


24 


86 


28 


100 


30 


.726 


24 


86 


28 


100 


21/2 


.627 


24 


86 


24 


100 


20 Vz 


.677 


24 


72 


28 


100 


43/2 


.727 


24 


86 


32 


100 


35 '/2 


.628 


24 


86 


28 


100 


36/2 


.678 


24 


72 


24 


100 


32 


.728 


24 


72 


24 


100 


24/2 


.629 


24 


86 


24 


100 


20 


.679 


24 


86 


32 


100 


40 Vi 


.729 


24 


86 


28 


100 


21 


.630 


24 


72 


24 


loo 


38 


.680 


24 


72 


24 


86 


43 


.730 


24 


72 


28 


100 


38/2 


.631 


24 


86 


32 


100 


45 


.681 


24 


72 


24 


100 


5\Vz 


.731 


24 


72 


24 


100 


24 


.632 


24 


86 


28 


too 


36 


.682 


24 


72 


28 


100 


43 


.732 


24 


86 


28 


100 


20/2 


.633 


24 


86 


24 


100 


19 


.683 


24 


86 


28 


100 


29 


.733 


24 


72 


24 


86 


38 


.634 


24 


72 


24 


100 


37/2 


.684 


24 


86 


2>2 


100 


40 


.734 


24 


86 


28 


100 


20 


.635 


24 


86 


24 


100 


l8'/2 


.685 


24 


72 


24 


86 


42 % 


.735 


24 


72 


28 


100 


38 


.636 


24 


86 


28 


100 


35 '/2 


.686 


24 


86 


28 


100 


28/z 


.736 


24 


86 


28 


100 


I9V2 


.637 


24 


86 


32 


too 


44'/2 


.687 


24 


72 


28 


100 


42»/t 


.737 


24 


64 


24 


100 


35 


.636 


24 


72 


24 


100 


37 


.688 


24 


72 


28 


100 


42/2 


.738 


24 


72 


24 


86 


37/2 


.639 


24 


86 


24 


100 


l7»/2 


.689 


24 


86 


32 


100 


39/2 


.739 


24 


72 


24 


100 


22/2 


.640 


24 


86 


28 


100 


35 


.690 


24 


86 


28 


100 


28 


.740 


24 


72 


28 


100 


37 & 


.641 


24 


86 


24 


100 


17 


.691 


24 


72 


24 


86 


42 


.741 


24 


86 


28 


100 


I8V2 


.642 


24 


86 


32 


100 


44 


.692 


24 


86 


28 


100 


27'/z 


.742 


24 


72 


24 


100 


22 


.643 


24 


86 


28 


100 


34 K* 


.693 


24 


72 


28 


100 


42 


.743 


24 


86 


28 


100 


Id 


.644 


24 


86 


24 


100 


16 


.694 


24 


86 


32 


100 


39 


.744 


24 


72 


24 


100 


21/2 


.645 


24 


86 


24 


100 


15/2 


.695 


24 


64 


24 


100 


39/z 


.745 


24 


72 


28 


100 


37 


.646 


24 


66 


24 


100 


15/2 


.696 


24 


86 


26 


100 


27 


.746 


24 


64 


24 


100 


34 


.647 


24 


86 


24 


100 


15 


.697 


24 


72 


24 


86 


41/2 


.747 


24 


86 


28 


100 


17 


.646 


24 


86 


32 


100 


43 /z 


.698 


24 


72 


28 


100 


41/2 


.748 


24 


72 


24 


86 


36 Vz 


.649 


24 


86 


24 


100 


14/2 


.699 


24 


86 


32 


100 


38'/2 


.749 


24 


86 


28 


too 


16/2 



380 



The Cincinnati Milling Machine Company 





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100 


36 Vz 


.800 


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72 


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too 


31 


.850 


24 


72 


24 


86 


14 


.751 


14 


86 


28 


100 


16 


.801 


24 


72 


24 


86 


30 y z 


.851 


24 


64 


24 


100 


19 


.751 


14 


72 


24 


100 


20 


.802 


24 


64 


24 


86 


40 


.852 


24 


72 


28 


100 


24 


.753 


24 


86 


31 


100 


31ft 


.803 


14 


86 


32 


100 


26 


.853 


24 


72 


24 


86 


23ft 


.754 


24 


72 


14 


100 


19 Vi 


.804 


18 


86 


32 


100 


39 % 


.854 


24 


86 


32 


100 


17 


.755 


14 


71 


18 


100 


36 


.805 


24 


72 


32 


100 


41 


.855 


24 


64 


28 


100 


35'/* 


.756 


14 


86 


28 


100 


l4'/z 


.806 


24 


66 


32 


too 


25'/z 


.856 


24 


86 


32 


too 


16 Vz 


.757 


14 


71 


24 


86 


35 ft 


.807 


24 


64 


24 


86 


39 Vz 


.857 


24 


64 


24 


86 


35 


.758 


24 


86 


28 


100 


14 


.808 


24 


72 


28 


100 


30 


.858 


14 


64 


24 


100 


17 ft 


.759 


24 


64 


24 


100 


32 '/z 


.809 


24 


64 


24 


too 


26 


.859 


24 


72 


14 


86 


22ft 


.760 


24 


71 


28 


100 


35 ft 


.810 


28 


86 


32 


100 


39 


.860 


24 


64 


28 


100 


35 


.761 


24 


86 


28 


100 


13 


.811 


24 


72 


32 


100 


40»/z 


.861 


24 


72 


28 


86! 37ft 


.762 


24 


72 


24 


86 


35 


.811 


24 


72 


28 


100 


29 fc 


.862 


24 


72 


28 


100 22 Vz 


.763 


24 


72 


24 


100 


17'/* 


.813 


24 


72 


24 


86 


29 


.863 


24 


64 


24 


100 16ft 


.764 


24 


86 


28 


100 


11 


.8t4 


24 


64 


24 


86 


39 


.864 


28 


86 


31 


100134 


.765 


24 


72 


24 


100 


17 


.815 


28 


86 


32 


100 


38ft 


.865 


14 64 


14 


100; 16 


.766 


24 


72 


24 


86 


34 ft 


.816 


24 


72 


28 


|00 


2S 


.866 


14 


86 


32 


100 14 


.767 


24 


72 


14 


100 


16ft 


.817 


24 


72 


24 


86 


28ft 


.867 


24 


64 


14 


IOOI5'/ 2 


.768 


14 


86 


18 


100 


10 ft 


.818 


24 


72 


28 


86 


41 


.868 


24 


72 


18 


100 


21ft 


.769 


24 


86 


18 


100 


10 


.819 


24 


86 


32 


100 


23 Vz 


.869 


24 


64 


14 


100 15 


.770 


24 


86 


32 


100 


30 ft 


.820 


24 


72 


28 


100 


28 ft 


.870 


24 


86 


32 


100 


13 


.771 


24 


72 


24 


86 


34 


.821 


24 


72 


24 


86 


28 


.871 


24 


64 


24 


too 


14 Vz 


.772 


24 


72 


24 


100 


15 


.822 


24 


86 


32 


too 


23 


.872 


24 


86 


32 


100 


11 Vz 


.773 


24 


86 


32 


100 


30 


.823 


24 


72 


32 


too 


39'/z 


.873 


24 


64 


24 


100 


14 


.774 


24 


71 


24 


100 


14 ft 


.824 


24 


72 


28 


\00 


28 


.874 


24 


72 


24 


86 


20 


.775 


24 


64 


24 


100 


30 ft 


.815 


24 


72 


24 


86 


ZlVz 


.875 


24 


86 


32 


100 


11% 


.776 


24 


72 


24 


100 


14 


.816 


28 


86 


32 


too 


37 Vz 


.876 


24 


64 


28 


100 


33ft 


.777 


24 


86 


32 


100 


29ft 


.817 


24 


72 


28 


100 


ZlVz 


.877 


24 


64 


24 


100 


13 


.778 


24 


71 


28 


100 


33ft 


.818 


14 


86 


32 


too 


22 


.878 


24 


86 


32 


100 


10ft 


.779 


24 


72 


14 


100 


13 


.829 


24 


86 


40 


100 


42 


.879 


24 


64 


24 


100 


11 Vz 


.780 


24 


72 


14 


86 


33 


.830 


24 


64 


24 


86 


37 ft 


.880 


24 


64 


24 


100 


12 


.781 


24 


72 


24 


100 


lift 


.831 


24 


72 


28 


86 


40 


.881 


24 


64 


18 


100 


33 


.781 


24 


72 


18 


100 


33 


.831 


24 


72 


24 


86 


26 ft 


.882 


24 


64 


24 


100 


lift 


.783 


24 


64 


24 


too 


29'/z 


.833 


24 


56 


24 


IOO 


36 


.883 


24 


64 


14 


86 


31 Vz 


.784 


24 


71 


14 


100 


lift 


.834 


24 


86 


32 


too 


21 


.884 


28 


86 


32 


too 


31 


.785 


24 


86 


32 


100 


28ft 


.835 


24 


72 


32 


100 


38 Vz 


.885 


24 


64 


14 


100 


10 ft 


.786 


18 


86 


31 


100 


41 


.836 


24 


72 


14 


86 


26 


.886 


24 


64 


14 


100 


10 


.787 


24 


64 


24 


too 


29 


.837 


24 


72 


28 


86 


39 Vz 


.887 


24 


71 


24 


86 


17 ft 


.788 


24 


72 


14 


100 


10 


.838 


24 


56 


24 


100 


35fe 


.888 


24 


64 


14 


86 


3Z 


.789 


24 


72 


24 


86 


31 


.839 


24 


86 


32 


100 


20 


.889 


24 


72 


14 


86 


17 


.790 


24 


64 


24 


86 


41 


.840 


24 


64 


24 


100 


21 


.890 


24 


72 


28 


100 


W/z 


.791 


24 


64 


24 


JOO 


28 ft 


.841 


24 


72 


32 


100 


38 


.891 


24 


56 


24 


IOO 


30 


.792 


24 


86 


32 


too 


ZT/z 


.842 


24 


86 


32 


too 


19ft 


.892 


24 


72 


14 


86 


16ft 


.793 


24 


71 


24 


86 


31ft 


.843 


24 


72 


28 


86 


39 


.833 


28 


86 


32 


IOO 


31 


.794 


24 


72 


28 


86 


43 


.844 


24 


86 


32 


IOO 


19 


.894 


24 


72 


24 


86 


16 


.795 


24 


72 


28 


too 


31 */z 


.845 


24 


72 


28 


too 


25 


.895 


24 64 


28 


100 


31ft 


.796 


24 


64 


24 


86 


40«/z 


.846 


24 


64 


24 


too 


20 


.896 


24 


72 


14 


86 


15 ft 


.797 


24 


72 


24 


86 


3| 


.847 


24 


86 


32 


too 


18 Vz 


.897 


24 


72 


28 


100 


16 


.798 28 


86 


32 


too 


40 


.848 


24 


64 


24 


100 


19'/* 


.898 


24 


72 


14 


86 


15 


.799| 24 


72 


32 


100 


4lft 


.849 


24 


86 


32 


100 


18 


.899 


24 


72 


28 


100 


\SVx 



A Treatise on Milling and Milling Machines 381 





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15 


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56 


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100 


22«/a 


1.001 


24 


56 


24 


100 


13 % 


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24 


72. 


24 


86 


14 


.952 


28 


86 


32 


100 


24 


1.002 


28 


86 


32 


100 


16 


.903 


24 


72 


28 


loo 


14 Vz 


.953 


24 


64 


24 


86 


24 ft 


1.003 


24 


56 


24 


100 


13 


.904 


24 


72 


24 


86 


13 Vz 


.954 


24 


56 


24 


100 


22 


1.004 


28 


86 


32 


100 


15/2 


.905 


24 


72 


28 


100 


14 


.955 


24 


72 


32 


100 


26/2 


1.005 


24 


56 


24 


100 


12/2 


.906 


24 


72 


24 


86 


13 


.956 


24 


64 


28 


86 


38'/2 


1.006 


24 


56 


24 


100 


12 


.907 


24 


72 


28 


100 


13/z 


357 


24 


56 


24 


100 


21/2 


1.007 


24 


64 


24 


86 


/6 


.908 


24 


72 


24 


86 


12 /z 


.958 


24 


72 


28 


86 


28 


1.008 


24 


56 


24 


100 


ll/z 


.909 


24 


72 


28 


100 


13 


.959 


24 


72 


32 


100 


26 


1.009 


28 


86 


32 


100 


14/2 


.910 


24 


72 


32 


100 


31 /z 


.960 


24 


64 


24 


86 


23/2 


1.0 10 


24 


56 


24 


100 


fl 


.911 


24 


72 


28 


100 


12 Vz 


.961 


24 


86 


44 


100 


38'A 


1.01 1 


28 


86 


32 


J00 


14 


.912 


24 


72 


28 


100 


12 


.962 


24 


72 


28 


86 


27/2 


L0I2 


24 


56 


24 


100 


10/2 


.913 


24 


72 


24 


86 


If 


.963 


28 


86 


32 


100 


22/2 


1.013 


24 


56 


24 


100 


10 


.914 


24 


72 


28 


100 


II Vz 


.964 


24 


56 


24 


100 


20/2 


1.014 


24 


64 


24 


86 


14/2 


.915 


24 


72 


32 


100 


31 


.965 


24 


64 


32 


100 


36/2 


1.015 


28 


86 


32 


100 


13 


.916 


24 


72 


24 


86 


10 


.966 


28 


86 


32 


J00 


22 


1.016 


24 


64 


24 


86 


14 


.917 


24 


72 


28 


100 


10/2 


.967 


24 


56 


24 


100 


20 


L0I7 


28 


86 


32 


100 


I2V2 


.918 


24 


64 


26 


100 


29 


.968 


24 


56 


24 


86 


36 


1.018 


24 


64 


24 


86 


OV2 


.919 


24 


72 


28 


100 


10 


.969 


24 


64 


28 


86 


37/2 


1.019 


28 


86 


32 


100 


12 


.920 


28 


86 


32 


100 


28 


.970 


24 


56 


24 


100 


(9/2 


1.020 


24 


64 


24 


86 


13 


.921 


24 


56 


24 


100 


26 Vz 


.371 


24 


72 


28 


86 


26/2 


(.021 


28 


86 


32 


100 


II Vz 


.922 


24 


64 


28 


86 


41 


.972 


86 


44 


32 


64 


6 


1022 


24 


64 


24 


86 


12/2 


.923 


24 


64 


28 


100 


28/2 


.973 


24 


56 


24 


100 


13 


1.023 


28 


86 


32 


100 


(( 


.924 


28 


86 


32 


100 


27/z 


.974 


24 


64 


24 


86 


21/2 


1.024 


24 


64 


24 


86 


12 


.925 


24 


56 


24 


100 


26 


.975 


24 


72 


32 


100 


24 


1.025 


24 


64 


28 


100 


(2/2 


.926 


24 


64 


32 


100 


39/2 


.976 


28 


86 


32 


100 


20/2 


1.026 


24 


64 


24 


86 


II/2 


.927 


24 


64 


26 


100 


28 


.977 


24 


64 


28 


100 


21 y2 


1.027 


24 


64 


28 


100 


12 


.928 


24 


64 


28 


86 


40/ 2 


.978 


24 


56 


24 


100 


|8 


1.028 


24 


64 


24 


86 


II 


.929 


24 


56 


24 


100 


25/2 


.979 


29 


86 


32 


100 


20 


1.029 


24 


64 


28 


100 


ll/z 


.930 


24 


72 


28 


86 


31 


.980 


24 


64 


28 


100 


21 


I.03O 


24 


64 


24 


86 


IO/2 


.931 


24 


64 


28 


100 


ZVh 


.981 


24 


64 


24 


86 


20/2 


1.031 


24 


64 


28 


100 


II 


.932 


28 


72 


32 


100 


41 '/2 


.982 


28 


86 


32 


100 


19/2 


1.032 


24 


64 


28 


\O0 


10/z 


.933 


24 


64 


24 


66 


27 


.983 


24 


72 


28 


86 


25 


L033 


24 


72 


32 


100 


14 /z 


.934 


24 


86 


44 


\00 


40/2 


.984 


24 


56 


24 


100 


17 


1.034 


24 


64 


28 


100 


10 


.935 


24 


72 


28 


86 


30/z 


.985 


28 


86 


32 


too 


19 


1.035 


24 


72 


32 


100 


14 


.936 


24 


56 


24 


100 


24/2 


.986 


24 


72 


32 


100 


22/2 


1.036 


24 


56 


24 


86 


30 


.937 


24 


64 


24 


86 


26'/ 2 


.987 


24 


64 


24 


86 


(9/2 


1.037 


24 


72 


32 


100 


13/z 


.938 


24 


72 


32 


100 


28/2 


.988 


28 


86 


32 


100 


(8'/2 


1.038 


24 


72 


28 


86 


17 


.939 


24 


64 


32 


too 


38/2 


.989 


24 


56 


24 


100 


16 


1.039 


24 


64 


32 


too 


30 


.940 


24 


56 


24 


100 


24 


.990 


24 


64 


24 


86 


19 


1.040 


24 


72 


32 


100 


13 


.94J 


24 


64 


24 


86 


26 


.991 


28 


86 


32 


100 


18 


1.041 


24 


56 


24 


86 


29/z 


.942 


24 


72 


32 


100 


28 


.992 


24 


56 


24 


100 


15/2 


1.042 


24 


72 


32 


100 


12/z 


.943 


24 


72 


32 


86 


40/2 


.993 


24 


64 


24 


86 


18/2 


1.043 


24 


72 


28 


86 


16 


.944 


24 


56 


24 


100 


Z"bVz 


.994 


24 


56 


24 


(00 


15 


1.044 


24 


72 


32 


100 


12 


.945 


24 


64 


24 


86 


25/2 


.995 


24 


72 


28 


86 


23/2 


1.045 


24 


86 


40 


100 


20/2 


.946 


24 


72 


32 


100 


27/2 


.996 


24 


56 


24 


(00 


14/a 


1.046 


24 


72 


32 


100 


ll/z 


.947 


24 


56 


24 


100 


23 


.997 


24 


56 


24 


86 


33/2 


1.047 


24 


72 


32 


100 


IJ 


.948 


28 


86 


32 


100 


24 Vz 


.998 


24 


56 


24 


100 


14 


1.048 


24 


72 


28 


86 


15 


.949 


24 


64 


24 


86 


25 


.999 


28 


86 


32 


100 


I6/2 


1.049 


24 


72 


32 


100 


10 /z 



382 



The Cincinnati Milling Machine Company 



WORM. 
^MEDIATE. 
RMEDIATE. 

SCREW. 


WORM. 
^MEDIATE. 


RMEDIATE. 
SCREW. 


. 


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L100 28 72 


32' 66 40 ft 


1.150 


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24 86 16 


1.0 51 24 72 32 100 10 


1.101 24 56 


24 86 23 


1.151 


24 


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32 100 16 ft 


1.052 24 86 40 100 19 ft 


LI02 24 64 


2S 86 25ft 


1.152 


28 


86 


44 100 36ft 


L053 24 72 28 86 14 


1.103 28 72 


32 100 27 ft 


LI 53 


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24 86 15ft 


1.0.54 24 72 28 86 14 


LI 04 24 86 


44100 26 


1.154 


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28 86 19 


1055 24 72 28 8613ft. 


1.105 24 56 


24 86 22 ft 


1.155 


24 


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24 86 15 


1.0 56 24- 56 24- 86 23 


LI 06. 40 64 


24100 42ft 


1.156 


24 


64 


32 100 15ft 


1,057 24 72 28 86 13 


1.107 24 64 


28 86 25 


1.157 


28 


72 


32 100 21ft 


1.0 58 24 86 40 100- 18 ft 


1.108 24 66 


44 100 25ft 


1.158 


24 


56 


24 86 14ft 


L059 24 72 28 86 12ft 


1.109 24 56 


24 86 22 


1.153 


24 


64 


32 100 15 


1.060 28 86 40100 35 '/a 


I.I 10 24 72 


32 86 26ft 


1.160 


24 


56 


24 86 14 


L06-I 24 72 28 86 12 


LI II 24 64 


28 86 24ft 


1.161 


24 


64 


28 86 18 


1,062 24 72 28 86-12 


LI 12 24 72 


40 100 33ft 


LI62 


24 


64 


32 100 14ft 


L063 24 72 28 86(11X2 


LI 13 24 56 


24 86 21ft 


LI63 


24 


56 


24 86 13ft 


L064 24 86 40 100 17ft 


1.114 24 64 


32 66 37 


LI64 


24 


64 


32 100 14 


1065 24 72 28 86.11 


LI 15 24 64 


28 86 24 


LI65 


24 


56 


24 66 13 


L066 24 56 24 66 27 


LI 16 24 56 


24 86 21 


LI66 


24 


72 


40 100 29 


L067 24 72 26 86 10 Vz 


1.117 24 86 


44 100 24ft 


1.167 


24 


64 


32 100 13ft 


L068 24 64 28 86 23 


LII8 28 72 


32 100 26 


1.168 


24 


56 


24 86 12ft 


1063 24 72- 28 86 10 


LI 19 24 72 


32 86 25ft 


1169 


24 


64 


32 100 13 


L070 24 86 40 100 16 ft 


LI20 24 56 


24 86 20ft 


1.170 


24 56 


24 86 12 


l.07| 32 56 24 100 38 ft 


LI2I 24 64 


32 86 36ft 


LI7I 


24 


64 


26 86 16 ft 


L072 28 72 32 10030 ft 


U22 24 86 


44 100 24 


1.172 


24 


56 


24 86 1 1 ft 


1.073 24 86 40 100 16 


1.123 23 72 


32 100 25ft 


1.173 


28 


72 


32 100 19ft 


L074 24 64 32 100 26 Vz 


1.124 24 56 


24 86 20 


1.174 


24 


56 


24 86 II 


L075 24 86 40 100 15ft 


LIES 28 64 


32 100 36ft 


LI75 


28 


86 


40 100 25ft 


L076 24 64 32 86 39 ft 


LI 26 24 86 


44100 23ft 


1,176 


24 


56 


24 86 10'ft 


L077 28 72 32 10030 


1.127 24 56 


24 86 left 


1.177 


24. 


64 


28 86 15 ft 


L078 24 86 40 100 15 


1.128 24 64 


32100 20 


1.178 


24 


56 


24 86 10 


1.079 24 56 24 86 25 ft 


LI29 24 64 


32 86 36 


L179 


24 


64 


28 86 15 


L080 24 86 40 100 14ft 


LI 30 24 72 


40 100 32 


LI80 


24 


64 


32 100 10 ft 


L 081 28 64 32 100 39ft 


1131 24 56 


24 86 19 


LISI 


32 


56 


2410030ft 


1.082 28 86 44100 41 


1.132 24 64 


28 86 22 


LI82 


24 


64 


32 100 10 


1.083 24 86 40 IOC 14 


LI33 24 72 


32 86 24 


LI83 


24 


86 44100 15ft 


1.084 24 56 24 86 25 


LI 34 24 56 


24 86 18ft 


1.184 


24 


64 


32 100 9ft 


1.065 24 86 44 100 13ft 


LI35 24 64 


32 100 19 


1.185 


24 


64 


28 86 14 


L086 28 86 40 100 33ft 


1.136 24 64 


28 66 21ft 


1.186 


24 


86 


44 100 15 


1.087 24 66 40 100 13 


LI37 24 56 


24 86 18 


LI87 


24 


64 


26 86 13ft 


1.088 24 56 24 86 24 h 


1.138 24 64 


32 100 18ft 


LI88 


24 


72 


40 100 27 


1.089 24 86 40 100 12ft 


1.139 28 86 


40 100 29 


LI 69 


24 


86 


44 100 14ft 


1.090 24 72 32 86 28ft 


L140 24 64 


26 86 21 


LI90 


24 


64 


28 66 13 


1.091 24 86 4S 100 35ft 


LI4I 24 56 


24 86 17 ft 


1191 


24 


86 


44 100 14 


1.092 24 86 40 100 12 


1.142 24 64 


32 86 35 


LI92 


24 


64 


26 86 12ft 


1093 24 56 24 86 24 


1,143 24 86 


44 100 21ft 


1193 


28 


72 


32 100 16ft 


L094 24 86' 40 100 lift 


1.144 24 56 


24 86 17 


1.194 


24 


64 


28 86 12 


L095 24 72 32 86 28 


1.145 28 72 


32 100 23 


LI95 


24 


72 


32 86 15ft 


1.096 24 86 40 100 II 


1.146 24 86 


44100 21 


1.196 


28 


72 


32 100 16 


1.09?; 24 86 40 100 10ft 


1.147 24 56 


24 86 16ft 


1.197 


24 


64 


28 86 lift 


1.098' 26 72; 32 100 28 

1.099 24 86 40 100, 10 


1.148 24 64 


32 100 17 


1.198 


24 


72 


32 86 15 


LI49 28 72. 


32 100:22ft 


1.199 


24 


±L 


28 86 II 



A Treatise on Milling and Milling Machines 383 







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CM 


< 


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wt 


<M 


O 


< 


_i 


O 


T+ 


cu 


O 


< 


1200 


24 


72 


32 


86 


14 /r 


1.25 


24 


64 


28 


72 


31 


1.300 


24 


86 


48 


100 


14 


1201 


24 


64 


28 


86 


lO'/i 


1.251 


24 


86 


48 


100 


21 


1.301 


24 


72 


40 


100 


12 Vz 


1 zoz 


24 


64 


28 


86 


10 


1.252 


28 


86 


40 


100 


16 


1.302 


24 


64 


32 


86 


21 


1.203 


24 


86 


44 


100 


II/2 


1.253 


24 


72 


40 


100 


20 


1.303 


24 


86 


48 


100 


13 Vz 


1.204 


28 


72 


32 


100 


l4*/z 


1.254 


24 


64 


32 


86 


26 


1.304 


24 


72 


40 


too 


12 


1205 


24 


86 


44 


100 


II 


1.255 


28 


86 


40 


too 


15/z 


1.305 


24 


64 


28 


72 


26/z 


1206 


24 


72 


32 


86 


l3'/i 


1.256 


24 


64 


28 


72 


30/2 


1.306 


24 


72 


40 


100 


ll/z 


1.207 


24 


86 


44 


100 


10/*. 


1.257 


24 


72 


40 


100 


19/2 


1.307 


32 


56 


24 


100 


17/z 


1 208 


24 


72 


32 


86 


13 


1.258 


28 


86 


40 


100 


15 


1.308 


24 


72 


40 


100 


II 


1209 


24 


86 


44 


100 


10 


1.259 


24 


86 


48 


100 


20 


1.309 


28 


86 


44 


100 


24 


mo 


28 


n 


32 


100 


13'/* 


1.260 


28 


86 


40 


100 


l4Vz 


1.310 


24 


64 


28 


72 


26 


1 211 


24 


72 


32 


86 


l2'/2 


1261 


28 


86 


40 


100 


14 Vz 


1.31 1 


24 


72 


40 


100 


lO'/z 


1212 


28 


72 


32 


100 


13 


1.262 


32 


56 


24 


100 


23 


1.312 


40 


64 


24 


100 


29 


1213 


24 


72 


32 


86 


12 


1.263 


28 


86 


40 


100 


14 


1.313 


24 


72 


40 


100 


10 


1214 


24 


86 


48 


100 


25 


1.264 


24 


72 


40 


100 


18'/* 


1.314 


28 


86 


44 


100 


23/z 


1.215 


24 


72 


32 


86 


II Yz 


1.265 


28 


86 


44 


100 


28 


1.315 


24 


86 


48 


100 


II 


1.216 


32 


56 


24 


100 


27 /z 


1.266 


28 


86 


40 


100 


13/2 


1.316 


28 


64 


32 


100 


20 


LI 17 


24 


72 


32 


86 


fl 


1.267 


24 


86 


48 


100 


19 


1.317 


28 


72 


32 


86 


24'/* 


1218 


24 


72 


40 


100 


24 


1.268 


24 


72 


40 


100 


18 


1.318 


24 


86 


48 


100 


lO'/z 


1219 


24 


72 


32 


86 


10/z 


1.269 


28 


86 


40 


100 


13 


1.319 


24 


64 


32 


86 


19 


1.220 


28 


86 


40 


100 


20'/* 


1.270 


Z4 


72 


44 


100 


30 


1.320 


24 


86 


48 


100 


10 


1221 


24 


72 


3Z 


86 


10 


1.271 


28 


86 


40 


100 


12/2 


1.321 


32 


56 


24 


100 


15/2 


1.222 


24 


72 


40 


100 


23/2 


1.272 


28 


72 


32 


86 


28/2 


1.322 


28 


72 


32 


86 


24 


1.223 


28 


72 


32 


100 


10 •/* 


1.273 


2ft 


86 


40 


100 


12 


1.323 


24 


64 


32 


86 


16/2 


1224 


28 


86 


40 


100 


20 


1.274 


28 


86 


40 


100 


12 


1.324 


32 


56 


24 


100 


15 


1 225 


28 


72 


32 


100 


10 


1.275 


24 


72 


40 


100 


17 


1.325 


28 


86 


48 


100 


32 


1226 


24 


72 


48 


100 


40 


1.276 


28 


86 


40 


100 


1172 


1.326 


32 


86 


40 


100 


27 


1227 


28 


86 


40 


100 


19/2 


1.277 


28 


86 


44 


100 


27 


1.327 


32 


56 


24 


100 


l4'/2 


1 228 


28 


86 


44 


100 


31 


1.278 


28 


86 


40 


100 


II 


1.328 


28 


64 


32 


too 


18/2 


1229 


24 


86 


48 


100 


23/* 


1.279 


24 


64 


32 


86 


23/2 


1.329 


28 


86 


44 


100 


22 


1.230 


28 


64 


32 


100 


28 /z 


1.280 


28 


86 


40 


100 


10/2 


1.330 


32 


56 


24 


100 


14 


1231 


28 


86 


40 


100 


19 


1.281 


24 


72 


40 


100 


16 


1.331 


28 


64 


32 


100 


18 


1 232 


24 


72 


40 


100 


22 /* 


1282 


28 


86 


40 


100 


10 


1.332 


28 


64 


32 


100 


16 


1233 


32 


86 


40 


too 


34 


1.283 


26 


72 


32 


86 


27/2 


1.333 


32 


56 


24 


100 


13/2 


1 234 


24 


86 


48 


100 


23 


1.284 


24 


72 


40 


100 


15/2 


1.334 


24 


64 


32 


86 


17 


1235 


28 


86 


40 


100 


IB'/2 


1.285 


24 


72 


40 


100 


15/2 


1.335 


28 


64 


32 


100 


17/2 


1.236 


24 


72 


40 


wo 


22 


1.286 


40 


64 


24 


100 


31 


1.336 


32 


56 


24 


100 


13 


1.237 


32 


56 


24 


100 


25/ 2 


1.287 


24 


72 


40 


100 


15 


1.337 


28 


7Z 


32 


86 


22/2 


1238 


28 


86 


40 


100 


18 


1.288 


24 


72 


40 


100 


15 


1.338 


32 


56 


24 


100 


12/2 


1239 


24 


64 


32 


72 


42 


1.289 


24 


64 


32 


86 


22 Vz 


1.339 


32 


56 


24 


100 


12/2 


1.240 


24 


72 


40 


100 


21/z 


1.290 


24 


72 


40 


100 


14'/* 


1.340 


24 


72 


44 


100 


24 


1 241 


28 


86 


44 


100 


30 


1.291 


24 


72 


40 


100 


14 Vz 


1.341 


32 


56 


24 


100 


12 


1.242 


28 


86 


40 


100 


l7'/z 


1.292 


32 


56 


24 


100 


l9'/2 


1.342 


28 


64 


32 


100 


16/z 


1243 


32 


56 


24 


100 


25 


1.293 


24 


72 


40 


100 


14 


1.343 


32 


56 


24 


100 


11/2 


1.244 


24 


72 


40 


100 


21 


1.294 


24 


86 


48 


100 


15 


1.344 


24 


64 


32 


86 


15/2 


1 245 


28 


86 


40 


100 


17 


1.295 


28 


72 


32 


86 


26/z 


1.345 


24 


72 


44 


100 


23/ 2 


1.246 


32 


72 


40 


100 


45/* 


1.296 


24 


72 


40 


100 


13/2 


1.346 


32 


56 


24 


100 


II 


1 247 


24 


86 


48 


100 


21 Vz 


1.297 


24 


86 


48 


100 


14/2 


1.347 


24 


64 


32 


86 


15 


1.248 


28 


86 


40 


100 


16 'A 


1298 


24 


64 


32 


66 


21/2 


1.348 


32 


56 


24 


100 


10/2 


1 249 


24 


72 


40 


100 


20'/* 


1.299 


24 


72 


40 


100 


13 


1.349 


28 


64 


32 


100 


15/2 



384 



The Cincinnati Milling Machine Company 





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Z 


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or 


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or 


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or 


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or 


-i 


< 


< 


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■ 


< 


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< 


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< 


o 


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51 


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UJ 


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r-i 


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O 


< 


_l 


o 


r-l 


OJ 


o 


<: 


_j 


<2> 


r-» 


CVJ 


O 


< 


1.350 


32 


56 


24 


100 


10 


1400 


40 


64 


24 


100 


21 


1.450 


32 


86 


40 


100 


13 


1.351 


24 


64 


32 


86 


14 Vz 


1.401 


28 


72 


32 


86 


14 Vz 


1451 


28 


64 


32 


86 


27 


1.352 


28 


64 


32 


100 


15 


1.402 


28 


86 


44 


100 


12 


1.452 


40 


64 


24 


100 


14'/* 


1.353 


24 


72 


44 


86 


37'/z 


1.403 


24 


72 


44 


100 


17 


1.453 


32 


86 


40 


100 


12 Vz 


1.354 


24 


64 


32 


86 


14 


1.404 


28 


72 


32 


86 


14 


1.454 


28 


86 


48 


100 


21/2 


1.355 


28 


64 


32 


100 


14 Vz 


1.405 


24 


64 


28 


72 


15 ft 


1.455 


32 


86 


40 


100 


12 


1.356 


24 


64 


32 


86 


13 ft 


1.406 


28 


86 


44 


100 


II 


1.456 


24 


72 


40 


86 


20 


1.357 


24 


64 


28 


72 


21 % 


1.407 


28 


72 


32 


86 


13ft 


1.457 


24 


72 


40 


86 


10 


1.358 


28 


64 


32 


100 


14 


1.408 


24 


64 


28 


72 


15 


1.458 


32 


86 


40 


100 


lift 


1.353 


2.4 


64 


32 


86 


13 


1.409 


28 


86 


44 


100 


10 ft 


1.459 


40 


64 


24 


100 


13/2 


1.360 


28 


72 


32 


86 


20 


l.4»0 


28 


72 


32 


86 


13 


1.460 


24 


44 


32 


86 


44 


1.361 


28 


64 


32 


100 


13'/* 


1.4 II 


28 


86 


48 


100 


25 Vz 


1.461 


32 


66 


40 


100 


II 


1.362 


24 


64 


32 


86 


12 ft 


1.412 


24 


64 


28 


72 


14/2 


1.462 


40 


64 


24 


100 


13 


1.363 


28 


86 


44 


100 


18 


1.413 


28 


72 


32 


86 


I2'/Z 


1.463 


32 


86 


40 


100 


10/2 


1.364 


24 


64 


32 


86 


12 


1.414 


24 


72 


44 


100 


15/2 


1.464 


40 


64 


24 


100 


IZ'/2 


1.365 


24 


64 


32 


86 


12 


1.415 


28 


72 


32 


86 


12 


1.465 


32 


86 


40 


100 


10 


{.366 


24 


64 


28 


72 


20/z 


1.416 


24 


64 


44 


86 


42 Vz 


1.466 


24 


72 


4-0 


86 


19 


1.367 


24 


64 


32 


86 


lift 


1.417 


24 


72 


44 


100 


15 


1.467 


40 


64 


24 


100 


12 


1.360 


28 


7Z 


32 


86 


19 


1.418 


28 


72 


32 


86 


11/2 


1.468 


28 


64 


40 


100 


33 


1.369 


24 


64 


32 


86 


M 


1.419 


32 


86 


40 


100 


17ft 


1.469 


26 


86 


48 


100 


20 


1.370 


28 


86 


44 


100 


17 


1.420 


28 


72 


32 


86 


II 


1.470 


40 


64 


24 


100 


II Vz 


1.371 


24 


64 


32 


86 


10 ft 


1.421 


24 


64 


28 


72 


13 


1.471 


28 


72 


40 


100 


19 


1.372 


24 


64 


32 


86 


10 ft 


1.422 


40 


64 


24 


100 


18ft 


1.472 


40 


64 


24 


100 


II 


1.373 


28 


64 


44 


100 


44ft 


1.423 


28 


72 


32 


B6 


10/2 


1.473 


40 


64 


24 


100 


II 


1.374 


24 


64 


32 


86 


10 


1.424 


28 


64 


32 


86 


29 


1.474 


24 


72 


40 


86 


18 


1.375 


32 


86 


40 


100 


22 Vz 


1.425 


28 


72 


32 


86 


10 


1.475 


40 


64 


24 


100 


loft 


1.376 


28 


72 


32 


86 


18 


1.426 


24 


64 


28 


72 


12 


1.476 


2a 


72 


40 


100 


18/2 


1.377 


28 


64 


32 


100 


10ft 


1.427 


32 


86 


40 


100 


16/2 


1.477 


40 


64 


24 


100 


10 


1.378 


28 


86 


44 


100 


16 


1.428 


28 


86 


48 


100 


24 


1.478 


24 


72 


40 


86 


17/2 


1.379 


28 


64 


3Z 


100 


10 


1.429 


24 


64 


28 


72 


II Vz 


1479 


24 


64 


32 


72 


27/z 


1380 


28 


72 


32 


86 


17/2. 


1.430 


32 


86 


40 


100 


16 


1.480 


28 


72 


40 


100 


18 


1.361 


28 


86 


44 


100 


15ft 


1.431 


24 


64 


28 


72 


II 


1.481 


28 


64 


32 


86 


24'/ 2 


1.382 


24 


64 


32 


72 


34 


1.432 


24 


72 


44 


100 


l2'/2 


1.482 


24 


72 


40 


86 


17 


1.383 


24 


64 


28 


72 


18ft 


1.433 


28 


86 


48 


100 


23ft 


1.483 


44 


64 


24 


100 


26 


1 384 


28 


86 


44 


100 


15 


1.434 


24 


64 


28 


72 


10/2 


1.484 


28 


72 


40 


100 


17/2 


1.385 


28 


64 


44 


100 


44 


1.435 


24 


72 


44 


loo 


12 


1.485 


24 


64 


32 


72 


27 


1.386 


40 


64 


24 


100 


22 ft 


1.436 


24 


64 


28 


72 


10 


I486 


24 


72 


40 


86 


16ft 


1.387 


28 


86 


44 


100 


14 ft 


1.437 


32 


86 


40 


100 


15 


1.487 


28 


86 


48 


100 


18 l 


1.388 


28 


64 


32 


86 


31 ft 


1.438 


24 


72 


44 


100 


lift 


1488 


28 


72 


40 


100 


17 


1.389 


32 


86 


40 


100 


21 


1.439 


28 


86 


48 


100 


23 


1489 


24 


72 


48 


100 


21ft 


1.390 


28 


86 


44 


100 


14 


1.440 


24 


72 


44 


100 


II 


1490 


24 


72 


40 


86 


16 


1.391 


28 


72 


32 


86 


16 


1.44/ 


32 


86 


40 


100 


|4ft 


1491 


28 


86 


48 


100 


17/2 


1.392 


44 


64 


24 


100 


32 ft 


1.442 


24 


72 


44 


100 


10/2 


1492 


28 


72 


40 


100 


16 ft 


1.393 


28 


86 


44 


100 


13 ft 


1.443 


24 


72 


44 


100 


10ft 


1.493 


28 


&4 


32 


86 


23/2 


1.394 


28 


72 


32 


86 


15ft 


1.444 


32 


66 


40 


100 


14 


1494 


24 


72 


40 


86 


I5V2 


1.395 


24 


72 


44 


100 


18 


1.445 


24 


72 


44 


100 


10 


1495 


28 


86 


48 


100 


17 


1.396 


28 


86 


44 


100 


(3 


1.446 


24 


72 


44 


86 


32 


1496 


28 


72 


40 


100 


16 


1 397 


24 


72 


44 


86 


35 


1.447 


32 


56 


40 


100 


\VSz 


1497 


24 


72 


40 


86 


15 


1398 


28 


72 


32 


86 


15 


1.448 


28 


72 


40 


100 


21/2 


1498 


32 


64 


40 


100 


41ft 


1.399 


28 


86 


44 


100 


!2'/z 


1.449 


40 


64 


24 


100 


15 


1.499 


28 


72 


40 


100 


15/2 



A Treatise on Milling and Milling Machines 385 







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< 


1.500 


lb 


64 


40 


100 


31 


1.550 


44 


64 


24 


100 


20 


1.600 


44 


56 


24 


100 


21 


1.501 


32 


86 


44 


too 


23 Vz 


1.551 


44 


64 


24 


100 


tZ 


1.601 


28 


64 


32 


86 


10/2 


1.502 


28 


86 


48 


100 


16 


1.552 


24 


72 


48 


100 


14 


1.602 


24 


64 


32 


72 


16 


1.503 


28 


72 


40 


100 


»5 


1.553 


28 


64 


32 


72 


37 


1.603 


28 


64 


32 


86 


10 


1.504 


24 


72 


40 


86 


14 


1.554 


24 


64 


40 


86 


27 


1.604 


32 


86 


44 


100 


11/2 


1.505 


24 


64 


32 


72 


25 Vz 


1.555 


44 


64 


24 


100 


19/2 


1.605 


40 


56 


24 


100 


20/2 


1.506 


26 


72 


40 


100 


14/2 


1.556 


24 


64 


32 


72 


21 


1.606 


24 


64 


32 


72 


15/z 


1.507 


24 


72 


40 


86 


ISVfe 


1.557 


28 


64 


32 


86 


17 


1.607 


32 


86 


44 


100 


II 


1.508 


24 


72 


48 


too 


19 Vz 


1.558 


24 


72 


44 


86 


24 


1.608 


44 


64 


24 


100 


13 


1.509 28 


64 


32 


86 


22 


1.559 


24 


72 


48 


100 


13 


1.609 


28 


72 


48 


100 


30/2 


1.510 


24 


72 


40 


86 


13 


1.560 


44 


64 


24 


100 


19 


1.610 


32 


86 


44 


100 


10/2 


1.51! 


24 


64 


32 


72 


25 


1.561 


28 


64 


32 


86 


16/2 


1.61 1 


44 


64 


24 


100 


12/2 


1.512 


24 


64 


44 


86 


38 


1.562 


24 


72 


48 


too 


l2'/2 


1.612 


32 


86 


44 


100 


10 


1.513 


24 


72 


40 


86 


12/2 


1.563 


28 


72 


44 


100 


24 


1.613 


28 


72 


44 


100 


19/2 


1.514 


24 


72 


48 


86 


35 / 2 


1.564 


24 


72 


44 


86 


23/2 


1.614 


44 


64 


24 


100 


12 


1.515 


28 


64 


32 


86 


21/2 


1.565 


24 


72 


48 


100 


12 


1.615 


24 


64 


48 


86 


39/2 


1.516 


24 


72 


40 


86 


12 


1.566 


32 


86 


44 


100 


17 


1.616 


40 


56 


24 


100 


19/2 


1.517 


24 


72 


48 


100 


!8'/2 


1.567 


28 


64 


44 


100 


35/2 


1.617 


44 


64 


24 


100 


ll'/2 


1.518 


32 


86 


44 


100 


22 


1.568 


24 


72 


48 


100 


II Vz 


1.618 


24 


64 


32 


72 


14 


1.519 


24 


72 


40 


86 


life 


1.569 


28 


64 


32 


86 


15/2 


1.619 


32 


86 


48 


100 


25 


1.520 


28 


86 


48 


100 


13 Vz 


1.570 


32 


72 


40 


100 


28 


1.620 


44 


64 


24 


100 


II 


1.521 


24 


72 


40 


86 


II 


1.571 


24 


72 


48 


100 


11 


1.621 


24 


64 


32 


72. 


13/2 


1.522 


24 


72 


40 


86 


11 


1.572 


28 


64 


32 


86 


15 


1.622 


44 


64 


24 


100 


10/2 


1.523 


28 


86 


48 


too 


13 


1.573 


24 


72 


46 


100 


10 Vz 


1.623 


28 


72 


44 


too 


18/2 


1.524 


24 


72 


40 


86 


10/2 


1.574 


32 


86 


44 


100 


16 


1.624 


24 


64 


32 


72 


13 


1.525 


28 


72 


40 


100 


11/2 


1.575 


24 


72 


44 


86 


22/2 


1.625 


44 


64 


24 


100 


10 


1.526 


24 


72 


40 


86 


10 


1.576 


24 


72 


48 


100 


10 


1.626 


24 


72 


44 


86 


17/2 


1.527 


28 


72 


40 


100 


II 


1.577 


32 


86 


44 


100 


15/2 


1.627 


24 


64 


32 


72 


12/2 


1.528 


32 


86 


44 


100 


21 


1.578 


44 


64 


24 


100 


17 


1.628 


24 


64 


32 


72 


12/2 


1.529 


28 


86 


48 


100 


12 


1.579 


28 


100 


56 


86 


30 


1.629 


32 


72 


40 


86 


38 


1.530 


28 


72 


40 


100 


10/2 


1.580 


28 


64 


32 


86 


14 


1.630 


24 


64 


32 


72 


\Z 


1.531 


28 


72 


44 


100 


26 '/2 


(.581 


32 


86 


44 


100 


15 


1.631 


24 


64 


32 


72 


12 


1.532 


28 


72 


40 


100 


10 


1.582 


44 


64 


24 


100 


16 Vz 


1.632 


28 


72 


44 


100 


l7'/2 


1.533 


32 


86 


44 


100 


20/2 


1.583 


28 


64 


32 


86 


13/2 


1.633 


28 


72 


40 


86 


25/2 


1.534 


28 


86 


48 


100 


II 


1.584 


40 


56 


24 


100 


22 & 


1.634 


24 


64 


32 


72 


1172 


1.535 


28 


64 


32 


86 


19/2 


1.585 


32 


86 


44 


100 


14/2 


1.635 


24 


72 


44 


86 


!6/2 


1.536 


32 


72 


40 


86 


42 


1.586 


28 


64 


32 


86 


13 


1.636 


24 


64 


32 


72 


II 


1.537 


28 


86 


48 


100 


IO'/2 


1.587 


24 


64 


40 


86 


24/2 


1.637 


32 


72 


40 


100 


23 


1.538 


24 


72 


48 


100 


16 


1.588 


32 


86 


44 


100 


14 


1.638 


32 


86 


48 


100 


23/2 


1.539 


28 


86 


48 


100 


10 


1.589 


28 


64 


32 


86 


l2'/2 


1.639 


24 


64 


32 


72 


10/2 


1.540 


28 


100 


56 


72 


45 


1.590 


44 


64 


24 


100 


15/2 


1.640 


28 


72 


40 


86 


25 


1.541 


40 


56 


24 


100 


26 


1.591 


32 


72 


40 


100 


26/z 


1.641 


28 


72 


44 


100 


16/2 


1.542 


24 


72 


48 


100 


15 »/a 


1.592 


28 


64 


32 


86 


12 


1.642 


24 


64 


32 


72 


10 


1.543 


32 


86 


44 


100 


l9'/2 


1.593 


24 


64 


40 


66 


24 


1.643 


24 


72 


44 


86 


15/2 


1.544 


28 


64 


32 


86 


16/2 


1.594 


44 


64 


24 


100 


15 


1.644 


24 


64 


40 


86 


19/2 


1.545 


24 


72 


48 


100 


15 


1.595 


28 


64 


32 


86 


11/2 


1.645 


28 


72 


44 


100 


16 


1.546 


24 


72 


46 


100 


15 


1.596 


28 


64 


44 


100 


34 


1.646 


28 


72 


40 


86 


24/2 


1.547 


40 


56 


24 


100 


25 Vz 


1.597 


44 


64 


24 


100 


14/2 


1.647 


24 


72 


44 


86 


15 


1.548 


28 


64 


32 


66 


18 


1.598 


28 


64 


32 


86 


II 


1.648 


40 


56 


24 


100 


16 


1.549 


24 


72 


48 


100 


14/2 


1.599 


24 


64 


40 


86 


23'/2 


1.649 


28 


72 


44 


100 


l5'/2 



386 



The Cincinnati Milling Machine Company 





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C\J 


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< 


1.650 


28 


64 


40 


100 


l9*/2 


1.700 


32 


72 


40 


100 


17 


1.750 


32 


86 


48 


100 


11/2 


1.651 


24 


72 


44 


86 


W/z 


1.701 


32 


64 


40 


86 


43 


1.751 


32 


72 


40 


100 


10 


1.652 


40 


56 


24 


100 


15/z 


1.702 


28 


64 


40 


100 


13/2 


1.752 


28 


100 


56 


86 


16 


1.653 


28 


72 


44 


100 


15 


1.703 


24 


64 


40 


86 


12/2 


1.753 


32 


86 


48 


100 


II 


1.654 


24 


72 


44 


86 


14 


1.704 


28 


64 


40 


72 


45/2 


1.754 


28 


72 


48 


100 


20 


1.655 


28 


64 


40 


100 


19 


1.705 


28 


64 


40 


100 


13 


1.755 


28 


72 


40 


86 


14 


1.656 


28 


72 


44 


100 


14 /z 


1.706 


24 


64 


40 


86 


12 


1.756 


32 


86 


46 


100 


10/2 


1.657 


28 


72 


44 


100 


14^ 


1.707 


40 


86 


44 


100 


33/ 2 


1.757 


28 


100 


56 


86 


I5V2 


1658 


24 


72 


44 


86 


l3'/z 


1.708 


28 


64 


40 


100 


12/2 


1.758 


32 


72 


44 


100 


26 


1.659 


24 


64 


40 


86 


18 


1.709 


24 


64 


40 


86 


11/2 


1759 


32 


86 


48 


100 


10 


1.660 


28 


72 


44 


100 


14 


1.710 


28 


72 


40 


86 


19 


1.760 


28 


72 


48 


100 


19/2 


1.661 


24 


72 


44 


86 


13 


1.71 1 


32 


72 


44 


100 


29 


1.761 


28 


100 


56 


86 


15 


1.662 


32 


86 


48 


100 


21 Vz 


1.712 


24 


64 


40 


86 


II 


1.762 


28 


64 


32 


72 


25 


1.663 


40 


56 


24 


100 


14 


1.713 


32 


72 


40 


100 


15/2 


1.763 


28 


72 


40 


86 


13 


1.664 


28 


72 


44 


100 


13/2 


1.714 


32 


64 


40 


too 


31 


1.764 


24 


72 


48 


86 


18/2 


1.665 


24 


72 


44 


86 


l2'/2 


1.715 


24 


64 


40 


86 


10/2 


1.765 


28 


100 


56 


86 


14/2 


1.666 


28 


64 


32 


72 


31 


1.716 


28 


72 


40 


86 


18/2 


1.766 


28 


72 


40 


86 


Wh 


1.667 


28 


72 


44 


100 


13 


1.717 


32 


72 


40 


100 


15 


1767 


44 


56 


24 


100 


20/2 


1.668 


24 


72 


44 


86 


12 


1.718 


24 


64 


40 


86 


10 


1.768 


32 


72 


48 


100 


34 


1.669 


28 


64 


40 


100 


17/2 


1.719 


28 


72 


48 


100 


23 


1.769 


28 


72 


40 


86 


12 


1.670 


28 


72 


44 


100 


\ZVz 


1.720 


28 


72 


40 


86 


18 


1.770 


28 


72 


48 


100 


18/2 


1.671 


24 


72 


44 


86 


11/2 


1.721 


28 


64 


40 


100 


10/2 


1.771 


28 


72 


48 


100 


16/2 


167Z 


24 


64 


40 


86 


l6'/2 


1.722 


24 


44 


32 


86 


32 


1.772 


44 


56 


24 


100 


20 


1.673 


40 


56 


24 


100 


l2'/2 


1.723 


28 


64 


40 


|00 


10 


1.773 


28 


72 


40 


86 


11/2 


1.674 


24 


72 


44 


86 


II 


1.724 


28 


100 


56 


86 


19 


1.774 


24 


72 


48 


86 


17/2 


1.675 


28 


64 


44 


100 


29/2 


1.725 


32 


72 


40 


100 


14 


1.775 


24 


44 


32 


B>6 


29 


1.676 


24 


72 


44 


86 


tO'/a 


1.726 


24 


56 


40 


86 


30 


1.776 


28 


72 


40 


86 


II 


1.677! 28 


72 


44 


100 


life 


1.727 


32 


72 


44 


100 


28 


1.777 


32 


56 


40 


100 


39 


1.678 


28 


64 


40 


100 


l6'/2 


1.728 


32 


72 


40 


100 


13/2 


1.778 


44 


56 


24 


100 


19/2 


1.679 


24 


72 


44 


86 


10 


1.729 


32 


72 


40 


100 


13/2 


1.779 


28 


72 


40 


86 


10/2 


L680 


28 


72 


44 


too 


II 


1.730 


28 


72 


40 


86 


17 


1.780 


28 


100 


56 


86 


12/2 


1.681 


24 


64 


40 


86 


15/z 


1.731 


24 


72 


48 


86 


21/2 


1.781 


28 


72 


40 


86 


10 


1.682 


28 


72 


44 


100 


IO'/2 


1732 


32 


72 


40 


too 


13 


1.782 


32 


64 


40 


100 


27 


1.683 


40 


56 


24 


too 


II 


1.733 


32 


86 


48 


100 


14 


1.783 


28 


100 


56 


86 


12 


1.684 


32 


86 


48 


100 


19/2 


1.734 


28 


72 


40 


86 


16/2 


1.784 


24 


56 


40 


66 


26& 


1.685 


28 


72 


44 


100 


10 


1.735 


28 


72 


40 


86 


16/2 


1.785 


28 


72 


48 


100 


17 


1.686 


28 


64 


40 


100 


15^2 


1.736 


32 


72 


40 


100 


12/2 


1.786 


28 


100 


56 


86 


ll/z 


1.687 


32 


64 


40 


100 


32/2 


1.737 


32 


86 


48 


100 


13/2 


1.787 


32 


72 


44 


100 


24 


1.688 


40 


56 


24 


100 


10 


1.738 


32 


56 


40 


100 


40/2 


1.788 


24 


72 


48 


86 


16 


1.689 


32 


86 


48 


100 


19 


1.739 


32 


72 


40 


100 


12 


1.789 


28 


100 


56 


86 


II 


1.690 


28 


64 


40 


100 


15 


L740 


32 


86 


48 


100 


13 


1.790 


28 


100 


56 


86 


II 


1.691 


32 


72 


40 


100 


18 


1.741 


28 


72 


44 


86 


29 


1.791 


24 


64 


44 


86 


21 


1.692 


24 


64 


40 


86 


14 


1.742 


32 


72 


40 


100 


ll>2 


1.792 


28 


100 


56 


86 


10/2 


1.693 


24 


72 


48 


86 


24/2 


1.743 


28 


72 


40 


86 


I5>2 


1.793 


28 


too 


56 


86 


10/2 


1.694 


32 


72 


44 


100 


30 


1.744 


32 


86 


48 


100 


\ZVz 


1.794 


44 


56 


24 


100 


16 


1.695 


44 


56 


24 


too 


26 


1.745 


32 


72 


40 


100 


II 


1.795 


28 


100 


56 


86 


10 


1.696 


24 


64 


40 


86 


13/2 


1.746 


24 


64 


44 


86 


24/2 


1.796 


28 


64 


32 


72 


22/2 


1.697 


28 


72 


44 


86 


31/2 


1.747 


32 


86 


48 


100 


12 


1.797 


24 


72 


48 


86 


15 


1.698 


28 


64 


40 


too 


14 


1.748 


32 


72 


40 


100 


10/2 


1.798 


24 


64 


44 


86 


20/2 


1.699 


24 


64 


40 


86 


13 


1.749 


28 


72 


48 


100 


20/2 


1.799 


28 


72 


48 


100 


15/2 



A Treatise on Milling and Milling Machines 387 





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1.800 


^ 32 


72 


44 


100 


23 


1.850 


28 


64 


44 


100 


16 


1900 


28 


64 


40 


86 


21 


1.801 


24 


72 


48 


86 


14/2 


1.851 


44 


56 


24 


100 


11 


1.901 


28 


64 


32 


72 


12 


1.602 


28 


64 


32 


72 


22 


1.852 


28 


72 


44 


86 


21/2 


1.902 


28 


64 


32 


72 


12 


1.803 


28 


72 


48 


100 


15 


1.853 


28 


56 


32 


72 


33/2 


1.903 


28 


72 


44 


86 


17 


1.804 


32 


72 


44 


86 


37/i 


1.854 


44 


56 


24 


100 


10/2 


1.904 


24 


64 


48 


66 


24/2 


1.805 


24 


72 


48 


86 


14 


1.855 


28 


64 


44 


100 


15/2 


1.905 


28 


64 


32 


72 


11/2 


1.806 


24 


56 


40 


86 


25 


1.856 


24 


64 


40 


72 


27 


1.906 


32 


72 


44 


100 


13 


1.807 


28| 72 


48 


100 


14/z 


1.857 


44 


56 


24 


100 


10 


1.907 


32 


64 


40 


100 


17/2 


1.808 


Z& 


72 


48 


100 


14 /a 


1.858 


24 


64 


44 


86 


14/2 


1.908 


28 


64 


32 


72 


II 


1.809 


24 


72 


48 


86 


13>fe 


1.859 


28 


64 


44 


100 


15 


1.909 


32 


72 


48 


100 


26/2 


1.810 


28 


72 


48 


86 


33 & 


1.860 


32 


72 


44 


100 


18 


1.910 


32 


72 


44 


100 


12/2 


1.81 1 


28 


72 


48 


100 


14 


1.861 


24 


56 


40 


86 


21 


1.91 1 


24 


56 


40 


86 


I6/2 


1.812 


24 


72 


48 


86 


13 


1.862 


24 


64 


44 


86 


14 


1.912 


28 


64 


32 


72 


10/z 


1.813 


44 


56 


24 


100 


16 


1.863 


24 


56 


40 


86 


20/a 


1.913 


32 


72 


44 


100 


12 


1.814 


24 


64 


44 


86 


19 


1.864 


28 


64 


44 


100 


14/2 


1.914 


28 


64 


32 


72 


10 


1.815 


28 


72 


48 


100 


13/2 


1.865 


32 


72 


44 


100 


17/2 


1.915 


28 


64 


32 


72 


10 


1.816 


24 


72 


48 


86 


12 /a 


1.866 


24 


64 


44 


86 


13/2 


1.916 


24 


56 


40 


86 


16 


1.817 


44 


56 


24 


100 


I5>* 


1.867 


32 


64 


40 


100 


21 


1917 


32 


72 


44 


100 


II/2 


1.818 


26 


72 


44 


86 


24 


1.868 


28 


64 


44 


100 


14 


1.918 


28 


72 


44 


86 


15/2 


1.819 


24 


72 


48 


86 


12 


1.669 


28 


64 


32 


72 


16 


1.919 


24 


44 


32 


86 


19 


1.820 


24 


64 


44 


86 


18/2 


1.870 


24 


64 


44 


66 


13 


1.920 


32 


72 


44 


100 


II 


1.821 


28 


64 


32 


72 


20 /a 


1.871 


32 


72 


44 


100 


17 


1.921 


24 


56 


40 


86 


15/2 


1.822 


44 


56 


24 


100 


15 


1.872 


28 


64 


44 


100 


13/2 


1.922 


28 


72 


44 


86 


15 


1.823 


24 


72 


48 


86 


11/2 


1.873 


24 


64 


44 


86 


12/2 


1.923 


32 


72 


44 


100 


IO/2 


1.824 


40 


86 


44 


100 


27 


1.874 


24 


64 


44 


66 


12/2 


1.924 


28 


64 


40 


86 


19 


1.825 


24 


64 


44 


86 


18 


1.875 


32 


72 


44 


100 


16/2 


1.925 


24 


56 


40 


86 


15 


1.826 


24 


72 


48 


86 


II 


1.876 


28 


64 


44 


100 


13 


1.926 


32 


72 


44 


100 


10 


1.827 


28 


64 


32 


72 


20 


1.877 


24 


64 


44 


86 


12 


1.927 


28 


72 


44 


86 


14/2 


1.828 


24 


56 


40 


86 


23 V* 


1.873 


28 


64 


32 


72 


15 


1.928 


28 


64 


44 


86 


30/2 


1.829 


24 


72 


48 


86 


10/2 


1,879 


28 


64 


44 


100 


12/2 


1.929 


24 


56 


40 


86 


14/2 


1.830 


28 


72 


48 


100 


life 


1.880 


24 


64 


44 


86 


M/z 


1.930 


24 


56 


40 


66 


14/2 


1.831 


28 


64 


44 


100 


18 


1.881 


32 


72 


40 


86 


24/2 


1.931 


28 


72 


44 


66 


14 


1.832 


24 


72 


48 


86 


10 


1.882 


28 


64 


32 


72 


14/z 


1.932 


32 


64 


40 


100 


15 


1.833 


28 


72 


48 


100 


II 


1.883 


28 


64 


44 


100 


12 


1.933 


48 


56 


24 


100 


20 


1.634 


44 


56 


24 


100 


13/2 


1.884 


24 


64 


44 


86 


II 


1.934 


24 


56 


40 


86 


14 


1.835 


24 


64 


44 


86 


17 


1.885 


32 


72 


44 


100 


I5V2 


1.935 


28 


72 


44 


86 


13/2 


1.636 


28 


72 


46 


100 


10/2 


1.886 


28 


64 


44 


100 


IIX2 


1.936 


32 


64 


40 


100 


14/2 


1.837 


28 


64 


40 


86 


25/2 


1.887 


24 


64 


44 


66 


10/2 


1.937 


28 


64 


48 


86 


37 '/i 


1.838 


44 


56 


24 


too 


13 


1.888 


28 


72 


44 


86 


18 Vz 


1.938 


24 


56 


40 


86 


13/2 


1.839 


28 


72 


48 


100 


10 


1889 


32 


72 


44 


100 


15 


1.939 


28 


72 


44 


86 


13 


1.840 


24 


64 


44 


86 


16/2 


1.890 


24 


64 


44 


66 


10 


1.940 


28 


64 


48 


too 


22/a 


1.641 


44 


56 


24 


100 


12/2 


1.891 


32 


64 


40 


100 


19 


1.941 


32 


64 


40 


100 


14 


1.842 


32 


72 


40 


86 


27 


1.892 


32 


72 


48 


100 


27/2 


1.942 


24 


56 


40 


86 


13 


1.843 


28 


64 


48 


86 


41 


1.893 


28 


64 


44 


100 


10/2 


L943 


28 


72 


44 


86 


12/2 


1.844 


28 


64 


32 


72 


18/2 


L894 


28 


64 


32 


72 


13 


1.944 


32 


56 


40 


86 


43 


1.845 


44 


56 


24 


100 


12 


1.895 


24 


56 


40 


86 


18 


1.945 


48 


56 


24 


100 


19 


1.846 


28 


64 


44 


100 


16/2 


1.896 


28 


64 


44 


100 


10 


1.946 


28 


72 


44 


86 


12 


1.847 


24 


44 


32 


86 


24/2 


1.897 


32 


64 


40 


100 


I8/2 


1.947 


28 


72 


44 


86 


12 


1.848 


44 


56 


24 


100 


11/2 


1.898 


28 


64 


32 


72 


12/2 


1.948 


32 


72 


40 


86 


19/2 


1.849 


24 


64 


44 


86 


15/2 


1.699 


28 


72 


46 


86 


29 


1.949 


24 


56 


40 


66 


12 



388 



The Cincinnati Milling Machine Company 





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1.950 28 


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life 


2.000 


48 


56 


24'l00 


13 Vz 


2.050| 28' 64 


48100 12/2 


1.851 24 


44 32 86 


16 


2.001 


28 


64 


40 86 


10/2 


2.051 j 24 64 40 72 10 


l.952i 40 


861 44 


100 


17/z 


2.002 


40 


86 


44;IC0 


12 


2.052 28 64 


44; 86|23/i 


1.953 28 


72 44 


86 


II 


2.003 


28 


64 


44 86 


2 6 '/a 


2.053 28 72 


48 86! 19 


1.954 24 


64 48 


86 


21 


2.004 


28 


64 


40 86 


10 


2.054 


28 64 48;I00 12 


1.955 32 


72j 48 


86 38 


2.005 


28 


100 


56i 72 


23 


2.055 


24! 64| 48 86 II 


1.956 51 


72 48 


100 23 Vz 


2.006 


40 


86 


44JIO0 


ll'/z 


2.056 


40! 86 48100 23 


1.957 24 


64 40! 72 


20 


2.007 


40 


86 


48100 


26 


2.057 


40 44 


24 100 1914 


1.958 40 


86 44 100 


17 


2.008 


48 


56 


24jl00 


l2/ a 


2.058 


24; 64:48 86 IO/2 


1.959; 28 


72i 48 86 


25 Vz 


2.009 


40 


86 


44100 


II 


2.059 


28 72 


46 86 18/z 


l.96o! 28 


72 44 86 


10 


2.010 


32 


72 


40 86 


13/z 


2.060 32 72 48 100 15 


1.961 24 


44 32 86 


15 


2.011 


32 


72 


48 100! 19/2 


2.061 


24 64 


48 86 10 


1.962 48 


56 


241 100 


17 Vz 


2.012 


48 


56 


24 I00|l2 


2.062 


24 56 


40 72 30 


1.963; 24 


56 


40 86 


10 


2.013 


40 


86 


44 


100 I0J6 


2.063 


40 44 


24 100 19 


1.964 


24 


64! 401 72 19 Vz 


2.014 


32 


72 


40 


86:13 


2.064 


44 


48 


28 100 36/2 


1.965 


24 


44 32! 86' 14/z 


2.015 


40 


86 


48 


100 25/e 


2.065 


28 


64 


48 100 IO/2 


1.966 28 


641 40 86 15 


2.016 


40 


86 


44 


100 


10 


2.066 


32 


56 


40, 86 39 


1.967 32 


64, 40 100' 10/z 


2.017 


24 


64 


40 72 


14/2 


2.067 


32 


64 


44 100 20 


1.968 40 


86 44100 16 


2.018 


32 


72 


40 86 


12 Vz 


2.068 


28 


64 


48 100 10 


1.969 24 


64 40 72 19 


2.019 


48 


56 


24 100 


II 


2.069 


40 


44 


24; 100 18/z 


1.970 32 


64| 40 100 10 


2.020 


28 


72 


48 86 


21/2 


2.070 


32 


72 


48 100 14 


1.971 32 


72 


40 86 17/z 


2.021 


24 


64 


40 


72 


14 


2.071 


28 


72 


48 86 17/2 


1.972 


48 


56 


24 100 16 Vz 


2.022 


32 


72 


40 


86 


12 


2.072 


32 


56 


40 100 25 


1973 


40 


86 


44100 15/2 


2.023 


48 


56 


24 100 


10/2 


2.073 


28 64 


40l 72 31/2 


1.974 


24 


44 


32 86 13/z 


2.024 


28 


64 


48 100 


15/2 


2.074 


32 


72 48 100 13/2 


1.975 


28 


64 


40 86 14 


2.025 


32 


72 


40 1 86 


11/2 


2.075 


40 


44 


24jl00 18 


1.976 


28 


64 


44 86 


28 


2.026 


48 


56 


24'l00 


10 


2.076 


28 


72 


481 86 1? 


1977 


40 


86 


44 100 


15 


2.027 


28 


100 


56 72 


2114 


2.077 


28 


100 


56 72 17/2 


L978 


24 


44 


32 86 


13 


2.028 


28 


64 


481100 


15 


2.078 


32 


72 


48 100 13 


1.979 


28 


64 


40 86 


13/2 


2.029 


32 


72 


40 66 


II 


2.079 


40 


72 


44] 86 43 


1.980 28 


64 


481100 


19/2 


2.030 


24 


64 


40 72 


13 


2.080 


32 


64 


44IOO|l9 


1.981 


24 


64 


40 72 


18 


2.031 


24 


64 


48 j 86 


14 


2.081 


40 


44 


24;IOO;l7y2 


1982 


24 


44 


32 86 


12/2 


2.032 


32 


72 


40 86 


10 Vz 


2.082 


32 


72 


48 100112/2 


1983 


28 


64 


40 86 


13 


2.033 


28 


64 


48100 


14/2 


2.083 


28100 


56! 72 17 


1.984 


28 


48 


40! 86 


43 


2.034 


24 


64 


40 ! 72 


12/2 


2.084 28| 64 


40 72|3I 


L985 


24 


64 


48 86 


18/a 


2.035 


24 


64 


48 86 


13/2 


2.0851 24 64 


48 72 33/2 


1.986 


24 


44 


32 86 


12 


2.036 


32 


72 


40 86 


10 


2.086 32 


72 


48100 12 


1.987 


28 


64 


40 


86 


!2'/z 


2.037 


24 


64 


40 72 


12 


2.087 28 


72 


48 86 


16 


1.988 


28 


56 


32 


72 


26/2 


2,038 


28 


64 


48 100 


14 


2.088 26100 


56 72 


I6/2 


1.989 


24 


44 


32 86 


M/2 


2.039 


24 


64 


48 86 


13 


2.089 28 j 64 


44; 86 


21 


1.990 


28 


64 


40 86 


12 


2.040 


32 


72 


48:100 


17 


2.090 32 72 


48100 


IIVz 


1.991 


28 


64| 40; 86 


12 


2.041 


24 


64 


40 72 


1114 


2.09l| 28 44 


32 86 28 


1.992 


48 


56 24' 100 l4'/z 


2.042 


28 


64 


48100 


WA 


2.092; 28 72 


48 86 15/2 


1.993 


24 


44 


32 86 11 


2.043 


24 


64 


48 86 


12 Vz 


2.093 32 72 


44 86 23 


1.994 


28 


64 


40 86 ll'/z 


2.044 


40 


44 24100 


20 Vz 


2.094 32 72 


48 100 II 


1.995 


40 


86 


44100 13 


2.045 


24 


64 


401 72 


II 


2.095: 28 56 


32 72 19/2 


1.996 


24 


44 


32 86IO/2 


2.046 


28 


64 


48100 


13 


2.096 28 64 


44 86 20/2 


1.997 


32 


72 


40 86 15 


2.047 


24 


64 


48 86 


12 


2.097 32 72 


48 100 10/2 


1.998 


28 


64 


40 86 II 


2.048 


24 


64 


40 72 


10/2 


2.098 32 64 


44 100 17/2 


1.999 24 


44 


32 86,10 


2.049 


28 


64| 56 86 


44 


2.099 28,100 


56 72 !5'/2 



A Treatise on Milling and Milling Machines 



389 





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2.100 


28 


44 


32 


86 


ZT/z 


2.150 


32 


72 


44 


86 


19 


2.200 


24 


56 


40 


72 


22/2 


2.101 


32 


72 


48 


100 


10 


2.151 


28 


56 


32 


72 


14/2 


2.201 


28 


64 


44 


86 


10/2 


2.102 


28 


72 


48 


86 


14/2 


2.152 


32 


64 


44 


100 


12 


2.202 


32 


72 


44 


86 


14/2 


2.103 


40 


44 


24 


100 


15/2 


2.153 


56 


64 


28 


100 


28'* 


2.203 


32 


56 


40 


100 


15/2 


2.104 


28 


too 


56 


72 


15 


2.154 


24 


64 


44 


72 


20 


2.204 


28 


64 


44 


86 


10 


2.105 


40 


86 


48 


100 


19 Vz 


2.155 


44 


56 


32 


100 


31 


2.205 


48 


56 


32 


100 


36/a 


2.106 


28 


72 


48 


86 


14 


2.156 


32 


64 


44 


100 


ll/z. 


2.206 


32 


72 


44 


86 


14 


2.107 


28 


72 


48 


86 


14 


2.157 


40 


86 


48 


100 


15 


2.207 


44 


86 


46 


100 


26 


2.108 


40 


44 


24 


100 


15 


2.158 


24 


56 


40 


72 


25 


2.208 


32 


56 


40 


100 


15 


2.109 


28 


100 


56 


72 


14 Vz 


2.159 


28 


72 


56 


86 


31 Vz 


2.209 


24 


64 


44 


72 


15/2 


2.H0 


28 


64 


44 


86 


19 /z 


2.160 


32 


64 


44 


100 


II 


2.210 


48 


100 


56 


86 


45 


2.111 


28 


72 


48 


86 


13 /2 


2.161 


28 


56 


32 


72 


13/2 


2.211 


32 


72 


44 


86 


I3V2 


2.112 


40 


44 


24 


100 


14* 


2.162 


40 


86 


48 


100 


14/2 


2.212 


32 


64 


40 


86 


18 


2.115 


28 


100 


56 


72 


14 


2.163 


32 


64 


44 


100 


10/2 


2.213 


32 


56 


40 


100 


14/2 


2.114 


28 


56 


32 


72 


18 


2.164 


32 


64 


40 


86 


21/2 


2.214 


24 


64 


44 


72 


15 


2.115 


28 


72 


48 


86 


13 


2.165 


28 


56 


32 


72 


13 


2.215 


24 


56 


40 


72 


21/2 


2.116 


28 


64 


44 


86 


19 


2.166 


32 


64 


48 


too 


25;* 


2.216 


32 


72 


44 


86 


13 


2.117 


40 


44 


24 


100 


14 


2.167 


32 


64 


44 


100 


10 


2.217 


28 


44 


40 


86 


41/2 


2.118 


28 


100 


56 


72 


13/2 


2.168 


32 


56 


40 


100 


18/2 


2.218 


32 


56 


40 


100 


14 


2.119 


28 


56 


32 


72 


17!* 


2.169 


28 


56 


32 


72 


12/2 


2.219 


24 


64 


44 


72 


14/2 


2.120 


28 


72 


48 


86 


12/2 


2.170 


32 


72 


48 


86 


29 


2.220 


32 


72 


44 


86 


12/2 


2.121 


24 


56 


40 


72 


27 


2.171 


24 


44 


48 


86 


44 Vz 


2.221 


28 


64 


40 


72 


24 


2.122 


28 


100 


56 


72 


13 


2.172 


28 


64 


44 


86 


14 


2.222 


28 


64 


48 


86 


24/2 


2.123 


32 


72 


44 


86 


21 


2.173 


28 


56 


32 


72 


12 


2.223 


32 


56 


40 


100 


13/2 


2.124 


28 


72 


48 


86 


12 


2.174 


32 


56 


40 


100 


18 


2.224 


32 


72 


44 


86 


12 


2.IZ5 


32 


64 


44 


100 


15 


2.175 


32 


72 


44 


86 


17 


2.225 


28 


44 


32 


86 


20 


2.126 


28 


100 


56 


72 


12/2 


2.176 


56 


64 


32 


100 


39 


2.226 


44 


86 


48 


100 


25 


2.127 


28 72 


48 


86 


ll'/z 


2.177 


28 


56 


32 


72 


11/2 


2.227 


32 


56 


40 


100 


13 


2.128 


28 


64 


44 


86 


18 


2.178 


40 


72 


44 


100 


27 


2.228 


32 


72 


44 


86 


11/2 


2.129 


32 


64 


48 


100 


27 J* 


2.179 


44 


86 


48 


100 


27/2 


2.229 


24 


64 


44 


72 


13/2 


2.130 


28 


100 


56 


72 


12 


2.180 


40 


86 


48 


100 


I2V2 


2.230 


32 


64 


40 


86 


\6Vz 


2.131 


28 


72 


48 


66 


II 


2.181 


28 


56 


32 


72 


II 


2.231 


28 


64 


48 


86 


24 


2.132 


24 


64 


44 


72 


21/2 


2.182 


28 


72 


56 


86 


30*2 


2.232 


32 


72 


44 


86 


II. 


2.133 


24 


64 


44 


72 


21/2 


2.183 


56 


64 


28 


100 


27 


2.233 


24 


64 


44 


72 


13 


2.134 


28 


100 


56 


72 


ll'/2 


2.184 


24 


56 


44 


72 


33/2 


2.234 


44 


48 


28 


100 


29/2 


2.135 


28 


72 


48 


86 


101* 


2.185 


28 


56 


32 


72 


10/2 


2.235 


44 


86 


48 


100 


24/2 


2.136 


28 


56 


32 


72 


16 


2.186 


32 


72 


44 


86 


16 


2.236 


32 


72 


44 


86 


10/2 


2.137 


32 


72 


44 


86 


20 


2.187 


40 


72 


44 


100 


26/2 


2.237 


24 


56 


40 


72 


20 


2.138 


28 


72 


48 


86 


10 


2.188 


28 


56 


32 


72 


10 


2.238 


24 


64 


44 


72 


12/2 


2.139 


32 


64 


44 


100 


13^2 


^I89 


28 


64 


44 


86 


12 


2.239 


32 


72 


44 


86 


10 


2.140 


24 


56 


40 


72 


26 


2.190 


32 


56 


40 


86 


34/2 


2.240 


32 


56 


40 


100 


11/2 


2.141 


28 


56 


32 


72 


15^2 


2.191 


48 


100 


56 


86 


45/z 


2.241 


32 


64 


40 


86 


15/2 


2.142 


28 


100 


56 


72 


10/2 


2.192 


40 


86 


48 


100 


II 


2.242 


24 


64 


44 


72 


12 


2.143 


56 


64 


28 


100 


29 


2.193 


28 


64 


44 


86 


III* 


2.243 


28 


64 


44 


72 


33 


2.144 


40 


72 


48 


100 


36'* 


2.194 


28 


64 


40 


72 


25/2 


2.244 


32 


56 


40 


100 


II 


2.145 


28 


100 


56 


72 


10 


2.195 


28 


64 


48 


86 


26 


2.245 


28 


64 


56 


86 


38 


2.146 


28 


56 


32 


72 


15 


2.196 


40 


86 


48 


100 


10/2 


2.246 


24 


64 


44 


72 


ll'/z 


2.147 


40 


86 


48 


100 


16 


2.197 


28 


64 


44 


86 


II 


2.247 


32 


64 


40 


86 


15 


2.148 


44 


86 


48 


100 


29 


2.198 


44 


66 


48 


100 


26'/2 


2.248 


32 


56 


40 


100 


10/2 


2.149 


40 


44 


24 


100 


10 


2.199 


40 


86 


48 


100. 10 


2.249 


32 


72 


48 


86 


25 



390 



The Cincinnati Milling Machine Company 





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2.250 24 


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2.300 


24 


56 


40 


72 


15 


2.350 


28 


64 


44 72|28/i 


2.251 32 


56 


40 100 10 


2.301 


32 


64 


48,100 


16/2 


2.351 


28 


48 


40 7243/2 


2.252 32 


64 


40 86 14/2 


2.302 


28 


64 


48| 86 I9V2 


2.352 


32 


64 


48100 ll'/2 


2.253 ! 40 


64 


44 100 35 


2.303 


28 


44 


32 8613/2 


2.353 


32 


72 


48! 86 12/2 


2.254 24 


64 


44 72 10/z 


2.304 


28 


72 


56 86 24 Vx 


2.354 


28 


64 


40 1 72 14/2 


2.255! 32 


64 


48 100 20 


2.305 


24 


56 


40 72 14/2 


2355; 44 


86 


48100 16/2 


2.256| 28 


64 


48 8622/2 


2.306 


44 


56 


32:100123/2 


2.356 


32 


64 


48100 II 


2.257i 24 


64 44 72 10 


2.307 


28 


44 


32 


86 13 


2.357 


24 


64 48| 72 19/2 


2.258 28 


44 


32 86 17/2 


2.308 


44 


86 


48 


100 20 


2.358 


32 


56 


40 86 27/2 


2.259 32 


64 


44 86; 28 


2.309 


28 


64 


48 


86 


19 


2.359 


, 28 


64 


40 72 14 


2.260 : 44 


56 


32 100126 


2.310 


24 


56 


40 


72 


14 


2.360 


32 


64 


48l00'l0/2 


2.261 


44 


86 


48100 23 


2.311 


40 


72 


44 


100 


19 


2.361 


40 


72 


44 100 15 


2.262 


32 


64 


40 86 13/2 


2.312 


28 


44 


32 


86 


12/2 


2.362 


44 


56 


32 100 20 


2.263 


44 


72 


48 100 391/2 


2.313 


32 


64 


48 100 


15/2 


2.363 


32 


64 


44 86 23 


2.264 


40 


64 


4810041 


2.314 


44 


56 


32 100 


23 


2.364 


32 


64 


48100 10 


2.2651 28 


44 


32 8617 


2.315 


24 


56 


40 


72 


13/2 


2.365 


24 


56 


48 868/2 


2.266; 32 


64 


40 86 13 


2.316 


28 


44 


32 


86 


12 


2.366 


40 


72 


44 100 14/2 


2267 


28 


40 


32 86,29/1 


2.317 


24 


40 


44 


8641 


2.367 


56 


64 


2810015 


2.268 


40 


72 


48 8643 


2.318 


32 


64 


48 


100 15 


2.368 


24 


44 


40 86 21 


2.269 


32 


64 


48 100 19 


2.319 


26 


48 


44 


86139 


2.369 


28 


64 


40 72! 13 


2.270 


28 


44 


32 86 16/z 


2.320 


28 


44 


32 


86II/1 


2370 


44 


56 


32 100 l9'/2 


2.271 


32 


64 


40 86 12/2 


2.321 


28 


40 


32 


8627 


2371 


40 


72 


44100 14 


2.272 


28 


64 


48, 862l/i 


2.322 


28 


72 


56 


8623/2 


2.372 


56 


64 


28 100 14/2 


2.275 


44 


100 


56 86 37/2 


2.323 


48 


100 


56 


86'42 


2.373 


28 


64 


40 72 12'A 


2.274 


48 


56 


32 100 34 


2.324 


32 


64 


48 100 ! 14/2 


2.374 


32 


100 


56 72:17/2 


2.275 


32 


64' 40 86 12 


2.325 


28 


44 


32; 86 II 


2.375 


28 


64 


48j 86 13/2 


2.276 


28 


44 


32! 86!I6 


2.326 


24 


64 


48 72 21/2 


2.376 


40 


72 


44 100 13/2 


2.277 


24 


56 


40 72|I7 


2.327 


24 


44 


40 86'23/z 


2377 


56 


64 


28 100: 14 


2.278 


44 


56 


32 100 25 


2.328 


28 


44 


32 


86.10/z 


2.378 


28 


64 


40! 72' 12 


2.279 32 


64 


40 86111/2 


2.329 


24 


56 


40 


72 12 


2.379 


28 


64 


46 86 13 


2.280 28 


64 


44 72 31/z 


2.330 


40 


100 


56 


72 4IVi 


2.380 


32 


100 


56 72 17 


2.281 40 


64 


44 86 


44/i 


2.331 


28 


64 


40 


72 16/z 


2.381 


40 


72 


44 100 1 13 


2.282 28 


44 


32 86 


\5'A 


2.332 


28 


44 


32 


86 10 


2.382 


28 


64 


40, 1 72ill/2 


2.283! 32 


64 


40 86 


II 


2.333 


24 


56 


40 


72 ll'/z 


2.383 


44 


86 


48, 100 14 


2.2841 28 


64 


40 72 


20 


2.334 


24 


64 


48 


7221 


2.384 


28 


64 


48 86 ! 12/2 


2.285' 44 


86 


48 10 21/2 


2.335 


28 


64 


48 86 17 


2.385 


32 


72 


56 86 34^ 


2.286 28 


64 


44 72 31 


2.336 


44 


86 


48 100 18 


2.386 


28 


64 


40 ! 72 It 


2.287 32 


64 


40 86 IO/2 


2.337 


24 


56 


40 72! 11 


2387 


56 


64 


28100 13 


2.288 44 


56 


32 100; 24/2 


2.338 


32 


64 


48JI00 13 


2.388 


44 


86 


46 100 13/2 


2.289 


24 


56 


40 72 16 


2.339 


40 


64 


44 86 


43 


2.389 


28 


64 


48; 86; 12 


2.290 


24 


44 


40 86J25/z 


2.340 


24 


56 


48 72 


35 


2.390 


28 


64 


40 72 10/2 


2.291 


32 


64 


40 


86 10 


2.341 


24 


56 


40 72 


10/2 


2.391 


40 


72 


44100 12 


2.292 


28 


64 


40 


72 19/z 


2.342 


32 


64 


56 86 44 


2.392 


56 


64 


28100 12/2 


2.293 


28 


44 


32 


86 


l4'/z 


2.343 


56 


64 


28I00|I7 


2.393 


28 


64 


46 86II/2 


2.294 24 


56 


40 


72 


15/2 


2.344 


24 


56 


44 


72 26/2 


2.394 


28 


64 


40' 72il0 


2.295 32 


64 


48 100 


17 


2.345 


24 


56 


40 


72 10 


2.395 


40 


72 


44 IOO|ll'/2 


2.296 32 


72 


56; 86 37>2 


2.346 


32 


72 


48 


86 19 


2.396 


56 


64 


28 100 IZ 


2.297 40 


72 


44,100 20 


2.347 


44 


56 


32 


100 21 


2.397 


28 


64 


48 86 II 


2.298 28 


44 


32 


86 


14 


2.348 


32 


64 


48 


100 


12 


2.398 


44 


86 


48! 100 12/z 


2.299| 28 


64 


40 


72 


19 


2.349 


40 


72 


44 


100 


16 


2.399 


40 


lZ 2 


44 100; II 



A Treatise on Milling and Milling Machines 391 





2 

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1-4 


CVJ 


O 


< 


2.400 


56 64 


32 


100 


31 


2.450 


24 


64 


48 


72 


lift 


2.500 


28 


64 


48 


72 


31 


2.401 28 64 


48 


86 


IO/2 


2.451 


32 


100 


56 


72 


10 


2.501 


44 


48 


28 


100 


13 


2.402 44! 86 


48 


100 


12 


2.452 


28 


64 


44 


72 


23ft 


2.502 


32 


64 


44 


86 


12 


2.403 40| 72 


44 


100 


10ft 


2.453 


32 


64 


44 


86 


l6'/2 


2.503 


28 


48 


44 


86 


33 


2.404; 32| 100 


56 


72 


15 


2.454 


24 


64 


48 


72 


1) 


2.504 


28 


40 


32 


86 


16 


2.405 


28 64 


48 


86 


10 


2.455 


40 


72 


48 


100 


23 


2.505 


24 


56 


44 


72 


17 


2.406 


24 1 44 


40 86 


18ft 


2.456 


24 


44 


40 


86 


14 Vz 


2.506 


44 


48 


28 


too 


12ft 


2.407 


40j 72 


44 


100 


10 


2.457 


28 


72 


56 


86 


14 


2.507 


32 


64 


44 


86 


II & 


2.408 


28 72 


56 


86 


18 


2.458 


24 


64 


48 


72 


10ft 


2.508 


32 


64 


48 


86 


26 


2.409 


56, 64 


28 


100 


10 ft 


2.459 


44 


56 


32 


100 


12 


2.509 


32 


64 


48 


86 


26 


2.410, 32 100 


56 


72 


14 ft 


2.460 


28 


64 


48 


72 


32 & 


2.510 


28 


40 


44 


86 


45 Vz 


2.411 | 44 86 


48 


100 


II 


2.461 


44 


48 


28 


100 


|6»/2 


2.511 


28 


44 


48 


86 


45 


2.412 


32j 72 


48 


86 


13ft 


2.462 


24 


64 


48 


72 


10 


2.512 


32 


56 


44 


72 


44 


2.413 


56! 64 


28 


100 


10 


2.463 


28 


40 


32 


86 


19 


2.513 


32 


56 


40 


86 


19 


2.414 


28j 64 


44 


72 


25 ft 


2.464 


44 


56 


32 


100 


ir/2 


2.514 


40 


72 


48 


100 


19 ft 


2415 


44] 86 


48 


too 


10ft 


2465 


32 


64 


44 


86 


15ft 


2.515 


32 


64 


44 


66 


IO/2 


2.416 


28 


64 


56 


86 


32 


2.466 


32 


56 


44 


86 


32 Vz 


2.516 


44 


48 


28 


100 


II/2 


2.417 


32 


72 


48 


86 


13 


2.467 


28 


72 


56 


86 


13 


2.517 


56 


64 


32 


100 


26 


2.418 


32 


64 


40 


72 


29 ft 


2.468 


44 


56 


32 


100 


II 


2.518 


24 


56 


44 


72 


16 


2.419 


44 


86 


48 


100 


10 


2.469 


24 


56 


44 


72 


19 Vz 


2.519 


32 


64 


44 


86 


10 


2.420 


32 


100 


56 


72 


l3'/2 


2.470 


28 


40 


32 


86 


I8V2 


2.520 


44 


48 


28 


too 


II 


2.421 


28 


72 


56 


86 


17 


2.471 


32 


64 


44 


86 


15 


2.521 


28 


48 


44 


72 


45 


2.422 


32 


72 


48 


86 


1214 


2.472 


44 


56 


32 


100 


10ft 


2.522 


28 


40 


32 


86 


14/2 


2.423 


44 


56 


32 


100 


15/2 


2.473 


32 


56 


40 


86 


21 ft 


2.523 


24 


56 


48 


72 


28 


2.424 


28 


40 


32 


86 


21/2 


2.474 


44 


48 


28 


100 


l5'/2 


2.524 


44 


48 


28 


100 


10ft 


2.425 


32 


too 


56 


72 


13 


2.475 


32 


64 


40 


72 


27 


2.525 


48 


56 


32 


100 


23 


2.426 


24 


64 


48 


72 


14 


2.476 


44 


56 


32 


100 


10 


2.526 


28 


64 


48 


72 


30 


2.427 


32 


72 


48 


86 


12 


2.477 


28 


72 


56 


86 


12 


2.527 


56 


64 


32 


100 


25ft 


2.428 


44 


56 


32 


100 


15 


2.478 


28 


40 


32 


86 


18 


2.528 


44 


48 


28 


100 


10 


2429 


32 


64 


48 


86 


29 ft 


2.479 


44 


48 


28 


100 


15 


2.529 


40 


72 


48 


100 


18 ft 


2.430 


32 


100 


56 


72 


l2'/2 


2.480 


44 


48 


28 


100 


15 


2.530 


24 


56 


44 


72 


15 


2.431 


32 


72 


48 


86 


II/2 


2.481 


28 


72 


56 


86 


lift 


2531 


40 


64 


44 


100 


23 


2.432 


28 


40 


32 


86 


21 


2.482 


24 


44 


40 


86 


12 


2.532 


28 


40 


44 


86 


45 


2.433 


44 


64 


46 


100 


42V2 


2.483 


28 


48 


40 


72 


40 


2.533 


28 


44 


46 


86 


44ft 


2.434 


28 


72 


56 


86 


16 


2.484 


28 


40 


32 


86 


l7'/2 


2.534 


48 


56 


32 


100 


22/2 


2.435 


32 


72 


48 


86 


II 


2.485 


28 


72 


56 


86 


II 


2.535 


32 


56 


40 


86 


17/2 


2.436 


24 


64 


48 


72 


13 


2.486 


48 


56 


32 


100 


25 


2.536 


40 


72 


56 


86 


45ft 


2437 


24 


56 


44 


72 


21 Vz 


2.487 


32 


64 


44 


86 


13/2 


2.537 


40 


72 


48 


100 


16 


2.438 


32 


56 


40 


86 


23'/2 


2.488 


28 


64 


44 


72 


21/2 


2.538 


28 


40 


32 


86 


13 


2.439 


32 


72 


48 


86 


10 Vz 


2.489 


44 


40 


32 


100 


45 


2.539 


28 


64 


56 


86 


27 


2.440 


32 


72 


48 


86 


IO/2 


2.490 


28 


72 


56 


86 


IO/2 


2.540 


32 


64 


48 


86 


24 & 


2.441 


24 


64 


48 


72 


12 Vz 


2.491 


44 


48 


28 


100 


14 


2.541 


24 


56 


44 


72 


14 


2.442 


28 


64 


56 


86 


31 


2.492 


32 


64 


44 


86 


13 


2542 


32 


56 


40 


86 


17 


2.443 


32 


72 


48 


86 


10 


2.493 


28 


72 


56 


86 


10 


2.543 


28 


64 


44 


72 


18 


2.444 


48 


56 


32 


too 


27 


2.494 


28 


72 


56 


86 


10 


2.544 


40 


72 


48 


100 


17ft 


2.445 


44 


56 


32 


100 


13/a 


2.495 


24 


44 


40 


86 


10/2 


2.545 


32 


56 


44 


86 


29/2 


2.446 


24 


64 


48 


72 


12 


2.496 


44 


48 


28 


100 


13^2. 


2.546 


24 


56 


48 


72 


27 


2.447 


32 


100 


56 


72 


10/2 


2.497 


32 


64 


44 


86 


12 Vz 


2.547 


24 


56 


44 


72 


13ft 


2.448 


44 


48 


28 


100 


17ft 


2.498 


24 


44 


40 


86 


10 


2.548 


24 


44 


46 


72 


45 Vz 


2.449 


56 


64 


32 


100 


29 


2.498 


24 


56 48 


72 


29 


2.549 


24 


44 


48 


72 


45ft 



392 



The Cincinnati Milling Machine Company 





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72 


17/*. 


2.600 


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56 


40 


86 


12 


2.650 


40 


56 


44 


86 


43/2 


2.551 


40 


72 


48 


100 


17 


2.601 1 26 


48 


40 


86 


le'/z 


2.651 


40 


56 


44 


86 


43 Vz 


2.552 


24 


56 


44 


72 


13 


2.602| 32 


64 


40 


72 


20*2 


2.652 


48 


64 


28 


56 


45 


2.555 


44 


40 


32 


100 


43/* 


2.603 40 


72 


56 


86 


44 


2.653 


40 


72 


44 


86 


21 


2.554 


28 


40 


44 


86 


44/ a 


2.604 


40 


72 


48 


100 


12 Vz 


2.654 


28 


56 


64 


86 


44 V z 


2.555 


32 


56 


40 


86 


16 


2.605 


32 


56 


40 


86 


11*2 


2.655 


56 


64 


32 


100 


16/2 


2.556 


40 


72 


48 


86 


34 /a 


2.606 


40 


56 


44 


86 


44*a 


2.656 


48 


56 


32 


100 


14X2 


2.557 


28 


40 


32 


86 


II 


2.607 


28 


48 


44 


72 


43 


2.657 


44 


40 


32 


100 


41 


2.558 


40 


72 


56 


86 


45 


2.608 28 


56 


64j 86 


45/2 


2.658 


28 


48 


40 


86 


11/2 


2.555 


40 


64 


44 


100 


ZWx 


2.609 32 


56 


40 


86 


II 


2.659 


24 


44 


48 


72 


43 


2.560 


32 


64 


48 


86 


23'/z 


2.610 


32 


64 


40 


72 


20 


2.660 


44 


48 


40 


100 


43/2 


2.561 


28 


40 


32 


86 


10/a 


2.611 


28 


64 


44 


72 


12/2 


2.661 


28 


4C 


44 


86 


42 


2.562 


24 


56 


44 


72 


12 


2.612 


40 


64 


48 


86 


4l/ 2 


2662 


48 


56 


32 


100 


14 


2.563 


28 


64 


48 


72 


28*2 


2.613 


32 


56 


40 


86 


10 Vz 


2.663 


48 


100 


56 


72 


44*2 


2.564 


28 


48 


44 


72 


44 


2.614 


32 


56 


40 


86 


IO'/2 


2.664 


32 


48 


40 


72 


44 


2565 


28 


40 


32 


86 


10 


2.615 


44 


48 


40 


100 


44/ 2 


2.665 


28 


64 


48 


72 


24 


2.566 


24 


56 


44 


72 


life 


2.616 


48 


100 


56 


72 


45/2 


2.666 


44 


100 


56 


86 21/2 


2.567 


32 


56 


40 


86 


15 


2.617 


48 


100 


56 


72 


45*2 


2.667 


40 


72 


56 


8642/2 


2.568 


40 


56 


48 


100 


41*2, 


2.618 


28 


44 


48 


86 


42/2 


2.668 


28 


48 


40 


86i 10/2 


2.569 


48 


56 


32 


100 


20 Vz 


2.619 i 32 


48 


40 


72 


45 


2.669 


32 


64 


48 


86! 17 


2.570 


44 48 


40 


ICO 


45*2 


2.620 


28 


64 


44 


72 


II/2 


2.670 


28 


48 


44 


72 


41*2 


2.571 


24 


44 


48 


72 


45 


2.621 


28 


48 


40 


86 


15 


2.671 


40 


72 


44 


86 


20 


2.572 


28 


64 


56 


86 


25 Vx 


Z622 


40 


72 


48 


100 


IO/2 


2.672 


40 


56 


44 


86 


43 


2573 


32 


56 


40 


86 


14 Vz 


2.623 


48 


56 


32 


IOC 


17 


2.673 


48 


56 


32 


100 


13 


2.574 


44 


40 


32 


100 


43 


2.624 


40 


72 


56 


66 


43/2 


2.674 


40 


64 


44 


100 


13/2 


2.575 


24 


56 


44 


72 


10/z 


2.625 


44 


56 


14 


64 


27 


2.675 


48 


64 


28 


56 


44*2 


2.576 


28 


40 


44 


86 


44 


2.626 


40 


72 


48 


100 


10 


2.676 


32 


64 


48 


86 


16*2 


2.577 


28 


64 


44 


72 


/5*2 


2.627 


40 


72 


48 


too 


10 


2.677 


28 


56 


64 


86 


44 


2.578 


48 


56 


32 


100 


20 


2.628 


40 


56 


44 


86 


44 


2.678 


48 


56 


32 


100 


12*2 


Z579 


24 


56 


44 


72 


10 


2.629 


28 


64 


44 


72 


105* 


2.679 


40 


64 


44 


100 


13 


2.580 


40 


72 


56 


86 


44 Vz 


2.630 


48 


56 


32 


100 


16 Vz 


2.680 


28 


44 


48 


86 


41 


2.581 


24 


44 


48 


86 


32 


2.631 28 


56j 64 86 


45 


2.681 


24 


44 


48 


72 


42*2 


2.582 


40 


72 


48 


100 


14'/* 


2.632 


28 


48| 40 86 


14 


2.682 


44 


48 


40 


ICC 


43 


2.583 


28 


64 


44 


72 


15 


2.633 


28 


64 


44 72 


10 


2.683 


48 


56 


32 


100 


12 


2.584 


32 


56 


40 


86 


13*2 


2.634 


32 


64 


40 ! 72 


18/2 


2.684 


44 


100 


56 


86 20/2 


2.585 


32 


56 


40 


86 


13*2 


2.635 


40 


72 


44 


86 


22 


2.685 


48 


100 


56 


72 44 


2.586 


28 


48 


44 


72 


435* 


2.636 


44 


40 


32 


100 


41/2 


2.686 


28 


64 


56 


86 I9'A 


2.587 


28 


48 


40 


86 


17*2 


2.637 


24 


44 


48 


72 


43*2 


2.687 


32 


48 


40 


72 43/t 


2.588 


40 


72 


48 


100 


14 


2.638 


44 


48 


40 


too 


44 


2.688 


48 


56 


32 


100! II/2 


2.589 


28 


64 


44 


72 


14/2 


2.639 


28 


44 


48 


86 


42 


2.689 


40 


72 


56 


86142 


2.550 


32 


56 


40 


86 


13 


2.640J 48 


100 


56 


72 


45 


2.690 


40 


64 


44 


100 12 


2.591. 


48 


100 


56 


86 


34 


2.641 


40 


100 


56 


64 


41 


2.691 


28 


48 


44 


72 41 


2.592 


40 


64 


44 


100 


19*2 


2.642 


32 


48 


40 


72 


44/2 


2.692 


40 


64 


48 


86 39/i 


2.593 


44 


48 


40 


100 


45 


2.643 


28 


48 


40 


86 


13 


2.693 


48 


56 


32 


100 


II 


2.594 


28 


64 


44 


72 


14 


2.644 


32 


72 


56 


86 


24 


2.694 


40 


56 


44 


86 


42*2 


2.595 


44 


40 


32 


100 


42 Vz 


2.645 


24 


40 


44 


86 


30/2 


2.695 


40 


64 


44 


100 


11*2 


2.596 


32 


48 


40 


72 


45*2 


2.646 


40 


72 


56 


86 


43 


2.696 


44 


40 


32 


100 


40 


2.597 


28 


40 


44 


86 


43*i 


2.647 


32 


64 


48 


86 


I8/2 


2.697 


48 


64 


28 


56 


44 


2.598 


28 


40 


44 86 4 3 /a 


2.648 56 


64 


32 


100 


19 


2.698 48 64 28 56 44 


2.599 


40| 72 


48100; 13 


2.643 28 


48| 44 


72J42 


2.699 28; 56 64 86 43'/z 



A Treatise on Milling and Milling Machines 393 





± 

O 


Si 

a 
u 

ft 


UJ 

Si 
o 

UJ 

7. 
01 


i 

UJ 

cr 
o 

CO 






Z 

or 
o 


o 

UJ 

z 


UJ 

< 
a 
UJ 
Z 
or 


i 

UJ 

or 
o 






£ 

or 
o 

> 


uJ 
Si 
o 

UJ 

or 

UJ 


ui 

< 
o 

Ul 


i 

UJ 

or 
o 
m 






z 


UJ 


u 


z 






z 


UJ 


UJ 


B 






z 


Ul 


z 






o 


h- 


H- 


o 


Id 




o 


/- 


H 


UJ 




o 


l- 


t- 


o 


UJ 


o 


K 


Z 


z 


ac 


_j 


o 


Or 


z 


Z 


or 


_J 


a 


Qc 


z 


z 


or 


_J 


< 


<t 


™" 


• 


< 


O 


< 


< 




■ 


< 


o 


< 


< 


— 


• 


< 


O 


UJ 


Ul 


fcl 


a 


UJ 


z 


UJ 


Ul 


» 


9 


UJ 


z 


UJ 


UJ 


fcl 


SI 


IS! 


z 


_l 


ci> 


i-» 


C\J 


O 


< 


_J 


e> 


r-t 


C\J 


o 


< 


_i 


O 


tH 


CJ 


< 


2.700 


28 


44 


48 


86 


40 Vz 


2.750 


28 


64 


48 


72 


19/2 


2.800 


24 


56 


48 


72 


lift, 


2.701 


48 


56 


32 


100 


10 


2.751 


40 


72 


56 


86 


40/2 


2.801 


28 


64 


56 


86 


10/2 


2.702 


24 


44 


48 


72 


42 


2.752 


48 


100 


56 


72 


42 Vz 


2.802 


28 


40 


44 


86 


38'A 


2.703 


28 


40 


44 


86 


41 


^753 


32 


48 


40 


72 


42 


2.803 


32 


64 


44 


72 


23 /a 


2.704 


44 


48 


40 


100 


42/2 


2.754 


44 


roo 


56 


86 


16 


2.804 


40 


64 


48 


86 


36/a 


2 70 5 


56 


64 


32 


100 


15 


2.755 


44 


40 


32 


100 


38/2 


2.805 


24 


56 


48 


72 


II 


2.70 6 


48 


40 


24 


100 


20 


2.756 


32 


56 


44 


86 


19/2 


2.806 


24 


44 


48 


72 


39/a 


2.707 


32 


64 


40 


72 


13 


2.757 


56 


64 


32 


100 


10 


2.807 


32 


56 


44 


72 


36/2 


2.708 


48 


100 


56 


72 


43 Va 


2.758 


40 


56 


44 


86 


41 


2.808 


28 


56 


64 


86 


41 


2.709 


32 


48 


40 


72 


43 


2.759 


44 


56 


24 


64 


20/* 


2.809 


48 


64 


28 


56 


41 /a 


2.710 


40 


72 


56 


86 


41/2 


2.760 


28 


44 


48 


86 


39 


2.810 


44 


56 


24 


64 


\7'A 


2.711 


28 


48 


44 


72 


40/i 


2.761 


44 


100 


56 


86 


15/2 


2.811 


44 


40 


32 


100 


37 


2.712 


32 


64 


40 


72 


12/2 


2.762 


40 


64 


48 


100 


23 


2.812 


40 


72 


56 


86 


39 


271?) 


32 


64 


48 


72 


35 Vx 


2.763 


28 


40 


44 


86 


39/2 


2.813 


40 


100 


56 


64 


36/a 


2.714 


32 


64 


48 


86 


13/2 


2.764 


28 


64 


56 


86 


14 


2.814 


32 


72 


56 


86 


13/a 


2.715 


40 


56 


44 


86 


42 


2.765 


48 


64 


28 


56 


42/2 


2.815 


28 


44 


40 


86 


18 


2.716 


44 


40 


32 


100 


39/2 


2.766 


24 


56 


48 


72 


14/2 


2.816 


32 


56 


48 


86 


28 


2.717 


32 


64 


40 


72 


12 


2.767 


44 


48 


40 


100 


41 


2.817 


48 


100 


56 


72 


41 


2.7/8 


40 


72 


44 


86 


17 


2.768 


44 


48 


40 


100 


41 


2.818 


48 


40 


28 


100 


33 


2.719 


32 


64 


48 


86 


13 


2.769 


40 


72 


44 


86 


13 


2.819 


44 


72 


48 


100 


16 


2.720 


48 


64 


28 


56 


43/2 


2.770 


28 


48 


44 


72 


39 


2.820 


40 


56 


44 


86 


39/2 


2.721 


28 


56 


64 


86 


43 


2.771 


28 


48 


44 


72 


39 


2.821 


44 


100 


56 


86 


10 


2.722 


32 


64 


40 


72 


II /a 


2.772 


40 


72 


56 


86 


40 


2.822 


28 


40 


44 


86 


38 


2.723 


24 


44 


48 


72 


41/2 


2.773 


32 


56 


44 


86 


18/2 


2.823 


28 


44 


40 


86 


17/a 


2.724 


28 64 


56 


86 


/7 


2.774 


48 


100 


56 


72 


42 


2.824 


28 


64 


48 


72 


14 /a 


2.725 


44 48 


40 


100 


42 


2.775 


40 


72 


44 


66 


12/2 


2.825 


32 


56 


44 


72 


36 


2726 


28 


48 


44 


86 


24 


2.776 


28 


64 


56 


86 


13 


2.826 


24 


44 


48 


72 


39 


2.727 


32 


64 


40 


72 


II 


2.777 


44 


56 


24 


64 


19/2 


2.827 


48 


40 


24 


100 


II 


2.726 


56 


64 


32 


100 


13 


2.778 


24 


56 


48 


72 


13/2 


2.828 


28 


48 


44 


72 


37/a 


2.729 


44 


72 


48 


100 


21/2 


2.779 


40 


56 


44 


86 


40/2 


2.829 


28 


56 


64 


86 


40tt 


2.730 


48 


100 


56 


72 


43 


2.780 


40 


72 


44 


86 


12 


2.830 


48 


64 


28 


56 


41 


2.731 


32 


48 


40 


72 


42/2 


2.781 


28 


64 


56 


86 


12/a 


2.831 


40 


72 


56 


86 


38/2 


2.732 


32 


64 


40 


72 


10 V% 


2.782 


48 


40 


24 


100 


15 


2.832 


40 


72 


56 


86 


38/2 


2.733 


32 


56 


44 


72 


38/2 


2.783 


28 


40 


44 


86 


39 


2.833 


44 


72 


48 


100 


15 


2.734 


56 


64 


32 


100 


/2/a 


2.784 


24 


56 


48 


72 


13 


2.834 


32 


64 


44 


72 


22 


2.735 


44 


40 


32 


100 


39 


2.785 


24 


44 


48 


72 


40 


2.835 


28 


48 


40 


72 


29 


2.736 


44 


40 


32 


100 


39 


2.786 


40 


64 


48 


86 


37 


2.836 


28 


44 


48 


86 


37 


2.737 


40 


56 


44 


86 


41/2 


2.787 


48 


64 


28 


56 


42 


2.837 


32 


48 


40 


72 


40 


2.738 


44 


72 


48 


100 


21 


2.788 


44 


48 


40 


100 


40/2 


2.838 


28 


44 


40 


86 


16/2 


2.739 


56 


64 


32 


100 


12 


2.789 


32 


56 


44 


72 


37 


2.839 


48 


100 


56 


72 


40 /a 


2.740 


28 


44 


48 


86 


39/2 


2.790 


28 


48 


44 


72 


38/2 


2.840 


40 


56 


44 


86 


39 


2.74/ 


28 


64 


48 


72 


20 


2.791 


40 


64 


48 


100 


2l'/2 


2.841 


28 


40 


44 


86 


37/a 


2.742 


32 


72 


64 


86 


34 


2.792 


40 


72 


56 


86 


39/2 


2.842 


28 


64 


48 


72 


13 


2.743 


48 


64 


28 


56 


43 


2.793 


44 


40 


32 


100 


37/a 


2.843 


32 


56 


44 


72 


35/a 


2.744 


24 


44 


48 


72 


41 


2.794 


40 


72 


44 


86 


10 /a 


2.844 


40 


72 


48 


86 


23/z 


2.74 5 


40 


72 


44 


86 


15 


2.795 


32 


48 


40 


72 


41 


2.845 


28 


44 


40 


86 


16 


2.746 


44 


48 


40 


100 


41 /i 


2.796 


48 


100 


56 


72 


41/2 


2.846 


24 


44 


48 


72 


38/a 


2.747 


44 


100 


56 


86 


16/2 


2.797 


28 


64 


56 


86 


11 


2.847 


28 


48 


44 


72 


37 


2.748 


32 


56 


44 


86 


20 


2.798 


28 


44 


48 


86 


38 


2.848 


44 


40 


32 


100 


36 


2.749 


32 


64 


48 


86 


10 a799 


40 


56 


44 


86 


40 


2.849 


40 


100 


56 


64 


35/a 



394 



The Cincinnati Milling Machine Company 



WORM 
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2.9CC 28 


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2 950 


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48 100 !0/2 


2 83, ab feA 2& 56 40* 


2 90! 4g,ICC 56 72 3? 


2951 


28 40 


44 86 34/i 


2 852 45- 64 25 5c 40fc 


2 502 26 


48 44 72 35 V* 


2.952 


26 56 


64 86 57 / 2 


2 855 28 64 48 72 12 


2.903 24 


44 45 86 17/j 


2953 


24 44 


43 86 14 


2 B54 28 4* ^5 86 36J* 


2 904 24 


44 48 72 37 


2.954 


40 64 


48 100 10 


2 855 28 44 4£ 86 36/k 


2 905 40 


72 48 66 20/2 


2.955 


46 64 


28 56 38 


2.656 24, 4C 44 £6 2/2 


2.906 28 


44 40 66 II 


2 956 


40 56 


44 86 36 


2 857 4: £4 4d 36135 


2.907 28 


48 44 86 13 


2957 


40 72 


48 86 17/2 


2.658 32 48 4C 72 39/z 


2.908 40 


72 56 66 36/2 


2958 


52 43 


40 72 37 


2853 26 44 cz 86 ,3 


2.909 44 


46 4C iOC 37/i 


2.959 


32 64 44 72 14/2 


2,860 4 56 4.4 66 56/i 


2910 28 


44 4C 86l0'/2 


2.960 


24 44 


43 72 35/2 


2 86! 28 48 46, 86 16/2 


2.9M 4C 


64 43 ICC 14 


2.96! 


28 44 


48 86 33/2 


2 862 32 64 44 72 ZZA 


2.912 28 


56 64 86 58/2 


2962 


4&'GC 


56 72 37/2 


2.862 28 64 4-S 72 1 1 


2913 28 


48 44 86 \l'A 


2 963 


40 56 


44100 19/2 


2.864 28 6* 4& 72 II 


2914 48 


64 28 56 39 


2.964 


40 72 


56 


86 35 


2.86 5 24 44 48 72 38 


2.915 28 


4C 44 86 3596 


2965 


32 64 


44 


72 14 


2.866 26 48 44 72 36Va 


2.916 44 


72 46 ICC 6 


2.966 


24 44 


48 


86 13 


2 867 4C ICC 36 64 35 


2,917 40 


64 46100 13/2 


2967 


44 48 


40 


100 36 


2 668 28 64 46 72 \ZA 


2.918 40 


56 44 8637 


2968 


40 100 


56 


64 32 


2869 44 72 46 ICC 12 


2.919 32 


48 40 72 58 


2.969 


28 4C 


44 


86 34 


2.87C 44 48 4C |0C 38/z 


2,920 28 


48 44 72 35 


2.370 


32 64 


46 


72 27 


2.871 28 56 64 86 35 A 


2.921 46 :CC 56 72 38/ 2 


2 97: 


24 40 


48 


86 27/2 


2 872 28 44 44 86 14 


2.922 46 ICO 56 72 38/2 


2972 


28 56 


64 


8637 


2.87 3 48 64 28 56 4 Q 


2 923 24 


44 48 72 36 ! /i 


2 973 


26 48 


44 72 33/2 


2,874 44 72 AS ICC WA 


2.924 26 


4 6 46 86 I1J% 


2974 


40 64 


48 86 3/2 


2,875 4C 64 48 86 34/ 2 


2925 4C 


64 48 86 33 


2.975 


4C 56 


44 &6 35/2 


2 876 44 56 24 64 12/z 


2.926 28 


44 46 86 34/ 2 


2976 


40 64 


44 86 2 A 


2.877 4c 64 48 ioc \6 l A 


2 927 40 


72 56 86 36 


2.977 


52 56 


44 72 2 A 


2 878 4C 64 56 86 45 


2 928 24 


4C 44 86 17/2 


2978 


32 43 


40 


72 36/2 


2 879 40 56 44 86 36 


2 929 44 


48 40 ICO 37 


2.979 


24 40 


44 


&6 14 


2 880 48 ICC 56 72 39/* 


2,930 32 


64 44 72 16/2 


2.580 


48 40 


28 


l0027/ 4 


2 881 48 IOC 56 72 39/ 2 


2.931 44 


56 46 ICC 59 


2.96: 


48 IO0 


56 


72 37 


2.882 44 86 24 64 12 


2.93*2 28 


56 64 86 58 


2.962 


40 72 


56 


86 34/2 


2 863 44 4C 32 ICC 35 


2 933 28 


40 44 86 35 


2.983 


24 44 


48 


86H/2 


2 884 28 46 44 72 56 


2.934 28 


48 44 86ICA 


2.984 


40 :0C 


56 


64 31/2 


2.885 24 44 46 72 37*i 


2.935 48 


64 28 56 38/2 


2.985 


44 48 


40 


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2.886 4C 64 44 66 25*1 


2.936 24 


40 44 8617 


2986 


26 4: 


44 


66 22/i 


2.887 44 56 24 64 i 1 / 2 


2 937 40 


56 44 86 36/2 


2987 


22 56 


4£ 


86 ZCA 


2.888 44 72 46 ICC 10 


2938 28 


48 44 72 34/2 


2988 


24 44 


48 86 


2.889 4C 72 56 86 37 


2939 32 


48 4C 72 37/z 


2 985 


32 6^ 


44 72 \z 


2890 44 46 4C ICC 38 


2 94 40 


64 48 ICC ll l /i 


? oar 


26 48 


44 72 32 


2.891 28 44 46 86 35/* 


2.941 24 


44 46 72 36 


299T 


28 56 


64 86 36 A 


2 892 28 56 64 86 39 


2.942 48 100 56 72 38 


2992 


44 56 


48 '.00 37/2 


2,893 40 S6 44 ICO 23 


2.943 32 


64 46 72 28 


2953 


4C 56 


44 8635 


2 894 48 64 26 56 39/;. 


2,944 28 


44 46 86 34 


2 594 


26 48 


40 72 22/2. 


2.695 32 56 44 72 34 


2 945 40 


72 56 86 35/2 


2995 


48 64 


28 56 37 


2.896 44 64 48 86 4; 


2.946 40 


72 56 86 35/2 


2996 


24 44 


48 72 34/2 


t 897 23 40 44 86 2*6 


2.947 24 


44 48 86 14/z 


2.997 


32 46 


40 72 36 


2.896 40 64 46 100 15 


2.948 44 


46. 4C ICC 36 A 


2.998 


24 44 


48 86 10 


2.899 40 56 44 86 37/z 


2 949 40 


72 46 86 18 


2959 


40 56 


48 100 29 



A Treatise on Milling and Milling Machines 395 





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31 


3.050 


40 


56 


44 


100 


14 


3.100 


24 


44 


48 


72 


31/2 


3.001 


48 


100 


56 


72 


36/2 


3.051 


40 


72 


56 


86 


32 /z 


3.101 


40 


72 


56 


86 


31 


3.002 


40 


72 


48 


86 


14 'A 


3.052 


32 


48 


40 


72 


34 /a 


3.102 


32 


44 


40 


86 


23/2 


3.003 


28 


40 


44 


86 


33 


3.053 


32 


48 


40 


72 


34/2 


3.103 


28 


56 


64 


86 


33/2 


3.004 


44 


48 


40 


100 


35 


3.054 


32 


56 


44 


72 


29 


3.104 


56 


44 


28 


86 


41 /i 


3.005! 40 


64 


48 


86 


30/2 


3.055 


56 


44 


28 


86 


42 '/a 


3.105 


40 


100 


56 


64 


27fe 


3006 


56 


44 


28 


86 


43'/* 


3.056 


28 


48 


44 


72 


31 


3.106 


32 


48 


40 


72 


33 


3.007 


28 


48 


44 


72 


32 Yz 


3.057 


32 


64 


48 


72 


23/i 


3.107 


32 


56 


48 


86 


13 


3.008 


24 


40 


44 


86 


II fe. 


3.058 


44 


48 


40 


100 


33/2 


3.108 


44 


40 


32 


100 


28 


3009 


32 


56 


44 


72 


30/2 


3.059 


40 


100 


56 


72 


10/2 


3.109 


48 


64 


28 


56 


34 


3.010 


28 


56 


64 


86 


36 


3.060 


28 


44 


48 


86 


30/2 


3.110 


44 


48 


40 


100 


32 


3.011 


40 


56 


44 


86 


34!/* 


3.061 


40 


100 


56 


64 


29 


3.111 


32 


56 


44 


72 


27 


3.012 


40 


100 


56 


72 


I4fe 


3.062 


40 


56 


44 


100 


13 


3.112 


32 


64 


48 


72 


21 


3.013 


40 


56 


44 


100 


l6'/2 


3.063 


48 


100 


56 


86 


life 


3.113 


48 


100 


56 


72 


33/2 


3.014 


48 


64 


28 


56 


36/2 


3.064 


40 


56 


44 


86 


33 


3.114 


32 


64 


56 


86 


17 


3.015 


48 


64 


28 


56 


36/2 


3.065 


40 


56 


44 


86 


33 


3.115 


28 


48 


40 


72 


16 


3.016 


32 


48 


40 


72 


35/a 


3.066 


32 


44 


40 


86 


25 


3.116 


40 


56 


44 


86 


31 Vz 


3.017 


40! 72 


56 


86 


33 Vz 


3.067 


28 


56 


64 


86 


34& 


3.117 


24 


44 


48 


72 


31 


3.018 


56! 48 


28 


100 


22/2 


3.068 


40 


72 


56 


86 


32 


3.118 


28 


48 


44 


72 


29 


3.019 


24! 40 44 


86 


IO/2 


3.069 


28 


40 


44 


86 


31 


3.119 


40 


100 


56 


64 


27 


3020 


48 100 


56 


72 


36 


3.070 


28 


40 


44 


86 


31 


3.120 


44 


64 


48 


100 


19 


3.021 


40 


64 


48 


86 


30 


3.071 


32 


48 


40 


72 


34 


3121 


28 


56 


64 


86 


33 


3.022 


44 


48 


40 


100 


34/2 


3.072 


48 


64 


28 


56 


35 


3.122 


44 


40 


32 


100 


27/2 


3.023 


28 


48 


44 


72 


32 


3.073 


32 


56 


48 


86 


15/2 


3.123 


28 


48 


40 


72 


15/2 


3.024 


32 


56 


44 


72 


30 


3.074 


48 


100 


56 


86 


10/2 


3.124 


32 


48 


40 


72 


32/2 


3.025 


40 


100 


56 


72 


13/a 


3.075 


44 


48 


40 


100 


33 


3.125 


32 


56 


44 


72 


26/2 


3.026 


28 


48 


40 


72 


21 


3.076 


48 


100 


56 


72 


34/ 2 


3.126 


44 


100 


56 


72 


24 


3.027 


40 


72 


48 


86 


12 /z 


3.077 


28 


44 


48 


72 


43/2 


3.127 


44 


48 


40 


100 


31/2 


3.028 


28 


44 


48 


86 


31/2 


3.078 


48 


100 


56 


86 


10 


3.128 


56 


44 


28 


86 


41 


3.029 


40 


56 


44 


86 


34 


3.079 


44 


40 


32 


too 


29 


3.129 


44 


64 


48 


100 


I8fe 


3.030 


40 


64 


44 


72 


37 /a 


3.080 


40 


64 


48 


86 


28 


3.130 


32 


56 


48 


86 


II 


3.031 


40 


100 


56 


64 


30 


3.081 


32 


56 


40 


72 


14 


3.131 


48 


100 


56 


72 


33 


3.032 


24 


44 


48 


72 


33 'A 


3.082 


40 


56 


44 


86 


32V2 


3.132 


40 


56 


44 


86 


31 


3.033 


44 


40 


32 


100 


30 /z 


3.083 


24 


44 


48 


72 


32 


3.133 


24 


44 


48 


72 


30/2 


3.034 


32 


48 


40 


72 


35 


3.084 


24 


44 


48 


72 


32 


3.134 


40 


64 


44 


86 


life 


3.035 


24 


40 


48 


86 


25 


3.085 


28 


56 


64 


86 


34 


3.135 


28 


44 


48 


86 


28 


3.036 


40 


64 


48 


86 


29/i 


3.086 


32 


44 


48 


86 


40/2 


3.136 


32 


56 


48 


86 


10/2 


3.037 


28 


40 


44 


86 


32 


3.087 


28 


48 


44 


72 


30 


3.137 


24 


40 


48 


86 


20/2 


3.038 


44 


64 


48 


100 


23 


3.088 


32 


64 


56 


86 


18/2 


3.138 


28 


56 


64 


86 


32/2 


3.039 


48 


100 


56 


72 


35/a 


3089 


32 


48 


40 


72 


33/2 


3.139 


32 


56 


44 


72 


26 


3.040 


44 


48 


40 


100 


34 


3.090 


48 


64 


28 


56 


34/2 


3.140 


32 


56 


48 


86 


10 


3041 


32 


56 


48 


86 


17/* 


3.091 


28 


44 


48 


86 


29/2 


3.141 


32 


48 


40 


72 


32 


3.042 


40 


64 


44 


86 


18 


3.092 


28 


48 


56 


86 


35/2 


3.142 


32 


64 


48 


72 


19/2 


3.043 


40 


100 


56 


72 


12 


3.093 


44 


48 


40 


100 


32/z 


3.143 


44 


48 


40 


100 


31 


3.044 


28 


44 


48 


86 


31 


3.094 


40 


64 


48 


86 


27/2 


3.144 


40 


64 


44 


86 


10/2 


3.045 


32 


64 


48 


72 


24 


3.095 


48 


100 


56 


72 


34 


314 5 


48 


64 


28 


56 


33 


3.046 


40 


100 


56 


64 


29/z 


3.096 


40 


64 


44 


86 


14/2 


3.146 


40 


100 


56 


64 


26 


3.047 


40 


56 


44 


86 


33/2 


3.097 


32 


56 


44 


72 


27/i 


3.147 


28 


40 


44 


86 


28/2 


3.046 


28 


56 


64 


86 


35 


3.098 


56 


48 


28 


100 


18/2 


3.148 


40 


56 


44 


86 


30/i 


3.049 


24 


44 


48 


72 


33 


3.099 


40 56 


44 


86 


32 


3.149 


48 


100 


56 


72 


32/z 



396 



The Cincinnati Milling Machine Company 





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< 


_J 


O 


t-i 


C\l 


O 


< 


_J 


O 


i-* 


C\l 


CD 


< 


3.150 


28 


44 


48 


86 


27/z 


3.200 


48 


100 


56 


72 


31 


3.250 


44 


64 


48 


100 


10 


3.151 


56 


44 


28 


86 


40 Vz 


3.201 


32 


64 


56 


86 


10/2 


3.251 


48 


72 


56 


86 


41/2 


3.152 


32 


56 


44 


72 


25/2 


3.202 


32 


56 


44 


72 


23/2 


3.252 


40 


72 


56 


86 


26 


3.153 


28 


44 


48 


72 


42 


3.203 


44 


40 


32 


100 


24X 2 


3.253 


44 


48 


40 


100 


27/2 


3.154 


32 


72 


64 


86 


17 'A 


3.204 


28 


48 


44 


72 


26 


3.254 


28 


56 


64 


86 


29 


3.155 


28 


64 


56 


72 


22 


3.205 


28 


40 


44 


86 


26/2 


3.255 


32 


46 


40 


72 


28/j 


3.156 


28 


56 


64 


86 


32 


3.206 


28 


56 


64 


86 


30/2 


3.256 


40 


56 


44 


86 


27 | 


3.157 


24 


40 


48 


86 


19/2 


3.207 


44 


48 


40 


100 


29 


3.257 


28 


48 


44 


72 


24 


3.158 


32 


48 


40 


72 


IVA 


3.208 


32 


48 


40 


72 


30 


3.258 


28 


40 


48 


86 


33/2 


3.159 


40 


100" 


56 


64 


25/2 


3.209 


40 


72 


56 


86 


27/2 


3.259 


28 


40 


44 


86 


24/2 


3.160 


44 


48 


40 


100 


30 Vz 


3.210 


24 


44 


48 


72 


28 


3.260 


32 


56 


44 


72 


21 


3.161 


40 


64 


48 


86 


25 


3.211 


40 


56 


44 


86 


28/2 


3.261 


40 


64 


48 


72 


38/2 


3.162 


28 


40 


44 


86 


28 


3.212 


56 


48 


28 


100 


10/2 


3.262 


44 


72 


48 


86 


17 


3.163 


48 


64 


28 


56 


32 / 2 


3.113 


48 


40 


28 


100 


17 


3.263 


24 


40 


48 


86 


13 


3.164 


40 


56 


44 


86 


30 


3.214 


48 


64 


28 


56 


31 


3.264 


48 


64 


28 


56 


29 Vz 


3.165 


24 


44 


48 


72 


29/a 


3.215 


40 


64 


48 


72 


39/2 


3.265 


48 


100 


56 


72 


29 


3.166 


48 


too 


56 


72 


32 


3.216 


48 


100 


56 


72 


30!4 


3.266 


40 


72 


56 


86 


25/ 2 


3.167 


24 


40 


48 


86 


19 


3.217 


56 


48 


28 


100 


10 


3.267 


44 


48 


40 


100 


27 


3.168 


40 


56 


48 


100 


22 '/ 2 


3.218 


28 


48 


44 


72 


25/2 


3.268 


24 


44 


48 


72 


26 


3.169 


40 


64 


48 


72 


40/a 


3.219 


28 


40 


44 


86 


26 


3269 


28 


48 


44 


72 


23'A 


3.170 


28 


48 


40 


72 


12 


3.220 


56 


44 


28 


86 


39 


3.270 


40 


56 


44 


86 


26/2 


3.171 


32 


72 


64 


86 


16/2 


3.221 


28 


48 


56 


86 


32 


3.271 


28 


40 


44 


86 


24 


3.172 


40 


100 


56 


64 


25 


3222 


28 


56 


64 


86 


30 


3.272 


32 


64 


48 


72 


II 


3.173 


28 


56 


64 


86 


3I'A 


3.223 


44 


48 


40 


100 


28/2 


3273 


44 


100 


56 


72 


17 


3.174 


40 


64 


48 


86 


24 Vz 


3.224 


32 


48 


40 


72 


29/2 


3.274 


48 


40 


28 


100 


13 


3.175 


32 


48 


40 


72 


31 


3.225 


24 


44 


46 


72 


271* 


3.275 


44 


40 


32 


100 


21/2 


3.176 


44 


48 


40 


100 


30 


3.226 


40 


56 


44 


86 


28 


3.276 


24 


40 


48 


86 


12 


3.177 


44 


40 


32 


100 


25/2 


3.227 


32 


64 


48 


72 


14!* 


3.277 


28 


40 


48 


86 


33 


3.178 


28 


44 


48 


86 


26'/2 


3.228 


44 


40 


32 


100 


23/2 


3.278 


40 


100 


56 


64 


20 Vz 


3.179 


32 


64 


56 


86 


12/2 


3.229 


32 


72 


64 


86 


12/2 


3.279 


40 


72 


56 


86 


25 


3.180 


40 


56 


44 


86 


29/2 


3.230 


48 


40 


28 


100 


16 


3.280 


48 


64 


28 


56 


29 


3.181 


28 


48 


40 


72 


II 


3.231 


48 


64 


28 


56 


30J* 


3.281 


48 


100 


56 


72 


28/2 


3.182 


28 


48 


40 


72 


II 


3.232 


32 


48 


44 


72 


37/a 


3.282 


44 


48 


40 


100 


26/i 


3183 


48 


100 


56 


72 


31/2 


3.233 


40 


100 


56 


64 


22/2 


3283 


32 


44 


40 


86 


14 


3.184 


44 


72 


48 


86 


21 


3.234 


40 


100 


56 


64 


22 & 


3.284 


40 


56 


44 


86 


26 


3185 


40 


100 


56 


64 


24/2 


3.235 


32 


72 


64 


86 


12 


3.285 


32 


48 


40 


72 


27/ 2 


3.186 40 


64 


48 


86 


24 


3.236 


28 


64 


56 


72 


18 


3.286 


44 


40 


32 


100 


21 


3.187! 28 


48 


40 


72 


IO'/2 


3 237 


28 


64 


56 


72 


18 


3287 


24 


40 


48 


86 


II 


3.1 88 ! 44 


64 


48 


100 


15 


3.238 


44 


48 


40 


100 


28 


3.288 


40 


64 


48 


86 


19/2 


3.I89J 32 


1 44 


40 


86 


19/2 


3.239 


32 


48 


40 


72 


29 


3.289 


40 


100 


56 


64 


20 


3.190! 28 


1 56 


64 


86 


31 


3240 


24 


44 


48 


72 


27 


3.290 


32 


44 


40 


86 


13/2 


3.191 ! 32 


48 


40 


72 


30/ 2 


3.241 


40 


56 


44 


86 


27 Vi 


3.291 


40 


64 


44 


72 


30/2 


3.192 44 


48 


40 


100 


29^ 


3.242 


24 


40 


48 


86 


I4'/i 


3.292 


40 


72 


56 


86 


24/2 


3.193 


44 


64 


56 


86 


44 y z 


3243 


56 


44 


28 


86 


38/2 


3293 


24 


40 


48 


86 


10/2 


3 194 


40 


72 


56 


86 


28 


3.244 


28 


48 


44 


72 


24/z 


3.294 


28 


48 


44 


72 


22/2 


3.195 


44 


72 


48 


86 


20/2 


3245 


28 


40 


44 


86 


25 


3.295 


24 


44 


46 


72 


25 


3.196 


40 56 


44 


86 


29 


3 246 


28 


40' 


44 


86 


25 


3296 


44 


48 


40 


100 


26 


3 197 


48 


64 


28 


56 


3l'/2 


3247 


44 


100 


56 


64 


32/2 


3297 


44 


40 


32 


100 


20/2 


3.198 


56 


44 


28 


86 


39 Vz 


3.248 


48 


64 


28 


56 


30 


3.298 


40 


56 


44 


86 


2 5 'A 


3.199 


40 


64 


48 


86 


23/2 


3.249 


48 


100 


56 


72 


29/2 


3.299 


40 


100 


56 


64 


19 'A 



A Treatise on Milling and Milling Machines 397 





I 

o 
2 


bi 
5 

o 
id 

z" 


u 

6 

o 

u 

ft: 


Id 
DC 
O 

to 






2 
a: 
o 

2 


Id 

o 

Id 


id 

fc 

o 
Id 
Z" 
ft: 


t 

Id 
K 
O 
CO 






or 



Id 

ii 

O 
Id 


!< 

O 

Id 

T 
ft 


i 

Id 
ft: 







z 


IU 


Id 


Z 






z 


Id 


Id 


z 






Z 


Id 


Id 


z 






o 


H 




o 


Id 




o 


h- 


\- 


o 


Id 




O 


Y- 


\- 





Id 


a 


tc 


Z 


Z 


or 


-J 


a 


or 


Z 


z 


ft: 


J 





ft: 


Z 


Z 


or 


_i 


< 


< 


~ * 


• 


< 


O 


< 


< 


^"* 


« 


< 


O 


< 


< 


■■" * 


• 


< 


O 


Id 


u 


fci 


SI 


Id 


z 


Id 


Id 


fcl 


zl 


Id 


z 


Id 


Id 


a' 


§1 


Id 


Z 


_J 


O 


»H 


C\l 


O 


< 


_l 


O 


tH 


(\J 


O 


< 


J 


O 


*H 


CM 


O 


< 


3.300 32 


48 40 72 


27 


3.350 


44 


48 


40 


100 


24 


3.400 


40 


56 


44 


86 


21 ft 


3.301 


28 


56 64 86 


27ft 


3.351 


40 


56 


44 


86 


23 ft 


3.401 


32 


64 


56 


72 


29 


3.302 


32 


56 


44 


72 


19 


3.352 


56 


48 


24 


64 


40 


3.402 


32 


56 


44 


72 


13 


3.303 


32 


44 


40 


86 


I2'ft 


3.353 


40 


64 


48 


86 


16 


3.403 


40 


100 


56 


64 


13ft 


3.304 


28 


44 


48 


86 


21 ft 


3.354 


28 


40 


44 


86 


20 ft 


3.404 


44 


56 


48 


100 


25'ft 


3.305 


40 


72 


56 


86 


24 


3.355 


48 


100 


56 


72 


26 


3.405 


28 


44 


48 


86 


16'ft 


3.306 


40 


64 


48 


72 


37 ft 


3.356 


48 


64 


28 


56 


26ft 


3.406 


24 


44 


48 


72 


20 ft 


3.307 


40 


64 


44 


72 


30 


3.357 


32 


48 


40 


72 


25 


3.407 


32 


44 


40 


72 


32ft 


3.308 


28 


40 


44 


86 


22/2 


3.358 


26 


56 


64 


86 


25 ft 


3.408 


44 


40 


32 


100 


14 ft 


3.309 


24 


44 


48 


72 


24 ft 


3.359 


28 


56 


64 


86 


25 ft 


3.409 


28 


48 


44 


72 


17 


3.310 


44 


48 


40 


100 


25ft 


3.360 


40 


56 


46 


too 


lift 


3.410 


32 


48 


40 


72 


23 


3.311 


48 


100 


56 


72 


27^2 


3361 


28 


48 


44 


72 


19 ft 


3.41! 


44 


72 


56 


86 


31 


3.312 


40 


56 


44 


86 


25 


3.362 


40 


56 


46 


86 


32 ft 


3.412 


46 


64 


28 


56 


24ft 


3.313 


44 


100 


56 


72 


14ft 


3.363 


44 


48 


40 


100 


23 ft 


3.413 


28 


44 


48 


86 


16 


3.314 


44 


56 


48 


100 


28/2 


3.364 


40 


56 


44 


86 


23 


3.414 


56 


40 


28 


86 


41ft 


3.315 


32 


48 


40 


72 


26 ft 


3.365 


28 


40 


44 


86 


20 


3.415 


28 


40 


44 


86 


17ft 


3.316 


28 


64 


56 


72 


13 


3.366 


40 


72 


56 


86 


21ft 


3.416 


32 


56 


44 


72 


12 


3.317 


28 


48 


44 


72 


21ft 


3.367 


28 


44 


48 


86 


18ft 


3.417 


24 


44 


48 


72 


20 


3.318 


40 


72 


56 


86 


23 ft 


3.368 


28 


44 


48 


86 


18ft 


3.418 


28 


48 


44 


72 


16ft 


3.319 


40 


100 


56 


64 


18ft 


3.369 


48 


100 


56 


72 


25 ft 


3.419' 


44 


64 


48 


86 


27 


3.320 


28 


40 


44 


86 


22 


3.370 


48 


64 


28 


56 


26 


3.420 


32 


40 


48 


86 


40 


3.3ZI 


32 


56 


44 


72 


18 


3.371 


32 


48 


40 


72 


24ft 


3.421 


40 


72 


56 


86 


19 


3.322 


28 


64 


56 


72 


12ft 


3.372 


28 


56 


64 


86 


25 


3.422 


32 


48 


40 


72 


22 ft 


3.323 


44 


48 


40 


100 


25 


3.373 


40 


100 


56 


64 


15ft 


3.423 


40 


56 


44 


86 


20ft 


3.324 


44 


72 


48 


86 


13 


3.374 


56 


44 


28 


86 


35 'ft 


3.424 


40 


64 


48 


86 


II 


3.325 


40 


56 


44 


86 


24 ft 


3.375 


44 


48 


40 


100 


23 


3.425 


28 


56 


64 


86 


23 


3.326 


48 


100 


56 


72 


27 


3.376 


40 


56 


44 


86 


22 ft 


3.426 


48 


64 


28 


56 


24 


3.327 


40 


64 


48 


86 


17ft 


3.377 


28 


44 


48 


86 


18 


3.427 


24 


44 


48 


72 


19ft 


3.328 


28 


48 


44 


72 


21 


3.378 


40 


72 


56 


86 


21 


3.428 


32 


56 


44 


72 


11 


3.329 


32 


48 


40 


72 


26 


3.379 


32 


56 


48 


72 


27ft 


3.429 


56 


40 


28 


100 


29 


3.330 


28 


56 


64 


86 


26 ft 


3.380 


32 


56 


48 


72 


27ft 


3.430 


28 


44 


48 


86 


15 


3.331 


56 


44 


28 


86 


36 ft 


3.381 


28 


48 


44 


72 


18 ft 


3.431 


40 


72 


56 


66 


16ft 


3.332 


28 


40 


44 


86 


21/2 


3.382 


40 


56 


48 


100 


9'ft 


3.432 


44 


56 


48 


100 


24ft 


3.333 


32 


64 


56 


72 


31 


3.383 


48 


100 


56 


72 


25 


3.433 


40 


64 


44 


72 


26 


3.334 


24 


44 


48 


72 


23 ft 


3.384 


32 


48 


40 


72 


24 


3.434 


40 


56 


44 


86 


20 


3.335 


28 


64 


56 


72 


lift 


3.385 


48 


64 


28 


56 


25ft 


3.435 


44 


48 


40 


100 


20 ft 


3.336 


40 


64 


48 


86 


17 


3.386 


28 


56 


64 


86 


24ft 


3.436 


48 


100 


56 


72 


23 


3.337 


44 


48 


40 


100 


24ft 


3.387 


28 


44 


46 


86 


17ft. 


3.437 


44 


40 


32 


100 


12/2 


3.338 


40 


56 


44 


86 


24 


3.388 


40 


56 


44 


86 


Zt 


3.438 


24 


44 


48 


72 


19 


3.339 


28 


48 


44 


72 


20ft 


3.389 


40 


72 


56 


86 


20 ft 


3.439 


48 


64 


28 


56 


23ft 


3.340 


40 


64 


44 


72 


29 


3.390 


48 


40 


32 


100 28 


3.440 


48 


100 


56 


64 


35 


3.341 


46 


64 


28 


56 


27 


3.391 


28 


48 


44 


72 


18 


3.441 


40 


72 


56 


86 


18 


3.342 


44 


72 


48 


86 


ll'ft 


3.392 


44 


40 


32 


too 


15ft 


3.442 


28 


40 


44 


86 


16 


3.343 


32 


48 


40 


72 


25 ft 


3.393 


44 


72 


56 


86 


31/2 


3.443 


28 


46 


44 


72 


15 


3.344 


28 


56 


64 


86 


26 


3.394 


24 


44 


48 


72 


21 


3.444 


40 


56 


44 


86 


19 ft 


3.345 


32 


44 


48 


86 


34 ft 


3.395 


32 


56 


44 


72 


13ft 


3.445 


28 


44 


48 


86 


14 


3.346 


28 


64 


56 


72 


10 ft 


3.396 


28 


40 


44 


86 


I8V2 


3.446 


44 


48 


40 


100 


20 


3.347 


24 


44 


48 


72 


23 


3.397 


32 


48 


40 


72 


23ft 


3.447 


40 


100 


56 


64 


10 


3.348 


44 


40 


32 


100 


18 


3.398 


48 


too 


56 


64 


36 


3.448 


24 


44 


48 


72 


18ft 


3.349 


28 


40 


48 


86 


31 


3.399 


28 


56 


64 


86 


24 


3.449 


48 


100 


56 


72 


22ft 



596 



The Cincinnati Milling Machine Company 



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3.489 

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32 46 4-C 
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72 54 

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86 17 
72 22 

56 21/2 
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66 35ft 

72 2'/2 
86 2. 
86 18 

72 4: 
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86 31 
72 IZ94 
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66 '3/2 
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86 173* 
72 16ft 
72 12 

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56 2 /2 
86 31/2 
86 24-/2 
72 [99ft 



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3525 

3.526 
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3 328 
3.529 
3530 
3.521 
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3,533 
3.534 
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3538 
3 539 
3 548 
3 541 
3.542 
3 543 
3 544 
3545 
3.546 
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3.546 
3.549 



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56 £6 

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3.553 

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3.557 
2538 
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3 36 
3 562 
3 563 

3 564 

3.565 
3.566 
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28 43 

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3.594 

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3 596 
3 597 
3598 
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64 86. 
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44 £6 

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28 72 
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64 £6 
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56 72 
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30 '-2 

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15/2 



A Treatise on Milling and Milling Machines 



399 





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100 


II 


3.650 


40 


72 


64 


66 


28 


3.700 


48 


40 


32 


100 


l5'/a 


3.601 


56 


40 


32 


100 


36/i 


3.65 \ 


48 


100 


56 


72 


12 


3.701 


28 


48 


56 


86 


13 


3.602 


32 


48 


40 


72 


13/2 


3.652 


40 


64 


44 


72 


17 


3.702 


44 


56 


48 


100 


II 


3.603 


28 


56 


64 


86 


14/z 


3.653 28 


56 


64 


86 


II 


3.703 


40 


64 


56 


86 


24/a 


3.604 


32 


40 


44 


72 


42 '/i 


3.654 


48 


64 


28 


56 


13 


3.704 


44 


56 


48 


72 


45 


3.605 


48 


64 


28 


56 


16 


3.655 


32 


64 


56 


72 


20 


3.705 


32 


56 


48 


72 


13/2 


3.606 


44 


48 


40 


100 


10/2 


3.656 


40 


56 


46 


86 


23^2 


3.706 


40 


64 


44 


72 


14 


3.607 


56 


44 


28 


66 


29 l A 


3.657 


44 


56 


48 


66 


33/2 


3.707 


32 


48 


44 


72 


24/2 


3.606 


48 


40 


32 


100 


20 


3.658 


46 


100 


56 


72 


M'/2 


3.708 


44 


56 


48 


100 


10/2 


3.609 


32 


48 


40 


72 


13 


3.659 


28 


56 


64 


86 


I0J/2 


3.709 


56 


44 


28 


86 


26ya 


3.610 


28 


56 


64 


86 


14 


3.660 


28 


48 


56 


86 


i5/2 


3.710 


44 


100 


56 


64 


15/2 


3.611 


44 


48 


40 


100 


10 


3.661 


48 


64 


28 


56 


12/2 


3.711 


40 


48 


44 


86 


29 /a 


3.612 


28 


48 


56 


86 


18 


3.662 


40 


64 


46 


72 


28/2 


3.712 


32 


56 


48 


72 


13 


3.613 


32 


56 


48 


72 


18/2 


3.663 


44 


72 


56 


86 


23 


3.713 


40 


64 


48 


72 


27 


3.614 


48 


100 


56 


72 


14 /a 


3.664 


28 


56 


64 


86 


10 


3.714 


44 


56 


48 


100 


10 


3.615 


32 


44 


40 


72 


26 Vz 


3.665 


48 


100 


56 


72 


II 


3.715 


28 


48 


56 


86 


12 


3.616 


32 


48 


40 


72 


\Z X A 


3.666 


32 


64 


56 


72 


19/2 


3.716 


28 


40 


48 


86 


18 


3.617 


44 


64 


48 


86 


19/a 


3.667 


44 


56 


48 


100 


13/2 


3.717 


56 


40 


28 


100 


18/a 


3.618 


28 


56 


64 


86 


13/2 


3.668 


48 


64 


28 


56 


12 


3.718 


48 


40 


32 


100 


14/a 


3.619 


32 


64 


56 


72 


21 X A 


3.669 


28 


48 


56 


86 


15 


3.719 


44 


100 


56 


64 


15 


3.620 


48 


40 


32 


100 


19/2 


3.670 


48 


100 


56 


72 


10/2 


3.720 


32 


56 


48 


72 


12/a 


3.621 


44 


72 


56 


86 


24/2 


3.671 


48 


100 


56 


72 


10/2 


3.721 


40 


64 


44 


72 


13 


3.622 


48 


100 


56 


72 


14 


3.672 


48 


40 


32 


100 


17 


3.722 


28 


46 


56 


86 


11/2 


3.623 


32 


48 


40 


72 


12 


3.673 


40 


64 


56 


86 


25/2 


3.723 


44 


64 


48 


86 


14 


3.624 


56 


44 


28 


86 


29 


3.674- 


44 


56 


48 


100 


13 


3.724 


32 


40 


44 


86 


24/2 


3.625 


44 


56 


48 


100 


16 


3.675 


48 


64 


28 


56 


11/2 


3.725 


56 


44 


28 


86 


26 


3.626 


28 


56 


64 


86 


13 


3.676 


48 


100 


56 


72 


10 


3.726 


48 


40 


32 


100 


14 


3.627 


40 


64 


48 


72 


29/* 


3.677 


28 


'48 


56 


86 


I4fc 


3.727 


32 


56 


48 


72 


12 


3.628 


44 


64 


48 


86 


19 


3.678 


44 


56 


48 


86 


33 


3.728 


28 


48 


56 


86 


II 


3.629 


44 


100 


56 


64 


19/2 


3.679 


40 


64 


48 


72 


28 


3.729 


40 


64 


48 


72 


26/2 


3.630 


32 


46 


40 


72 


11/2 


3.660 


32 


56 


48 


72 


15 


3.730 


48 


64 


32 


56 


29/2 


3.631 


48 


64 


26 


56 


14/2 


3.681 


48 


64 


28 


56 


II 


3.731 


44 


64 


48 


86 


13/2 


3.632 


28 


48 


56 


86 


17 


3.682 


44 


56 


48 


100 


12 /a 


3.732 


32 


44 


40 


72 


22/2 


3.633 


28 


56 


64 


86 


12 »A 


3.683 


28 


40 


48 


86 


19/2 


3.733 


32 


56 


48 


72 


ll/a 


3.634 


44 


56 


48 


100 


15/2 


3.684 


56 


40 


28 


100 


20 


3.734 


28 


48 


56 


86 


10/2 


3.635 


28 


40 


48 


66 


21/2 


3.685 


26 


48 


56 


86 


14 


3.735 


40 


64 


44 


72 


12 


3.636 


32 


48 


40 


72 


II 


3.686 


32 


44 


48 


72 


40/2 


3.736 


40 


64 


44 


72 


12 


3.637 


48 


100 


56 


72 


13 


3.687 


48 


64 


28 


56 


10^2 


3.737 


32 


56 


64 


86 


28/a 


3.636 


72 


56 


24 


64 


41 


3.688 


44 


64 


48 


86 


16 


3.738 


32 


64 


56 


72 


16 


3.639 


48 


64 


26 


56 


14 


3.689 


44 


56 


48 


100 


12 


3.739 


44 


64 


48 


86 


13 


3.640 


28 


56 


64 


86 


12 


3.690 


56 


48 


24 


64 


32 '/a 


3.740 


56 


44 


28 


86 


25/a 


3.641 


40 


56 


48 


86 


24 


3.691 


48 


40 


32 


100 


16 


3.741 


46 


44 


40 


100 


31 


3.642 


32 


48 


40 


72 


10/2 


3.692 


56 


44 


28 


86 


27 


3.742 


40 


64 


44 


72 


11/2 


3.643 


44 


56 


48 


100 


15 


3.693 


48 


64 


28 


56 


10 


3.743 


40 


64 


44 


72 


ir/2 


3.644 


48 


100 


56 


72 


12/2 


3.694 


28 


40 


46 


86 


19 


3.744 


44 


100 


56 


64 


13/2 


3.645 


48 


100 


56 


72 


12 Vx 


3.695 


44 


56 


48 


100 


ll/a 


3.745 


40 


64 


48 


72 


26 


3.646 


28 


56 


64 


86 


ll/a 


3.696 


40 


64 


48 


72 


27 /a 


3.746 


32 


56 


48 


72 


10/a 


3.647 


28 


40 


48 


86 


21 


3.697 


32 


56 


48 


72 


14 


3.747 


40 


64 


56 


86 


23 


3.648 


32 


48 


40 


72 


10 


3.698 


44 


56 


48 


86 


32/2 


3.748 


32 


64 


56 


72 


15 '/a 


3.649 


44 


64 


48 


86 


IB 


3.699 


32 


64 


56 


72 


ie> 


3.749 


40 


64 


44 


72|lf 



400 



The Cincinnati Milling Machine Company 





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3.750 


32 


44 


48 


86 


ZZ¥z 


3.800 


56 


44 


28 


86 


23/2 


3.850 


40 


64 


48 


72 22/i 


3.751 


44 


100 


56 


64 


13 


3.801 


40 


56 


48 


86 


17/2 


3.851 


48 


72 


56 


86 27/2 


1.75Z 


32 


56 


48 


72 


10 


3.802 


40 


56 


48 


86 


17/2 


3-852 


44 


72 


56 


86 14/2 


3.753 


44 


64 


48 


86 


12 


3.803 


32 


48 


44 


72 


21 


3.853 


32 


44 


40 


72 I7h. 


3.754 


32 


40 


44 


86 


23/2 


3.804 


32 


64 


56 


72 


12 


3.854 


56 


40 


28 


100 10/2 


3.755 


40 


64 


44 


72 


lO'/z 


3.805 


44 


72 


56 


86 


17 


3.855 


56 


40 


28 


100 10/2 


3.756 


56 


44 


28 


86 


25 


3.806 


48 


100 


56 


64 


25 


3.856 


40 


64 


56 


72 137/2 


3.757 


32 


64 


56 


72 


15 


3.807 


40 


64 


48 


72 


24 


3.857 


44 


72 


64 


S6 IZ 


3.758 


40 


56 


4b 


86 


l9'/i 


3.808 


32 


44 


40 


72 


19/2 


3.858 


32 


40 


44 


86 19/2 


3.759 


44 


100 


56 


64 


/2/i 


3.809 


28 


56 


64 


72 


31 


3.859 


40 


56 


48 


86 14/2 


3.760 


44 


64 


48 


86 


II/2 


3.810 


56 


40 


32 


86 


43 


3.860 


56 


40 


28 


100 10 


3.761 


40 


64 


48 


72 


25/4 


3.811 


32 


64 


56 


72 


ll'/2 


3.861 


56 


40 


28 


100 10 


3.762 


44 


72 


56 


86 


19 


3.812 


56 


40 


28 


100 


13/2 


3.862 


56 


44 


24 


64136 


3.763 


48 


40 


32 


100 


11/2 


3.813 


28 


44 


48 


72 


26 


3.863 


32 


44 


40 


72|I7 


3.764 


32 


44 


48 


86 


22 


3.814 


28 


40 


48 


86 


12/2 


3.864 


40 


64 


48 


72122 


3.765 


32 


64 


56 


72 


14/2 


3.815 


56 


44 


28 


86 


23 


3.865 


56 


40 


28 


86 32 


3.766 


44 


64 


48 


86 


It 


3.816 


32 


48 


44 


72 


20/a 


3.866 


48 


100 


56 


64123 


3.767 


44 


64 


48 


86 


II 


3.817 


48 


44 


40 


100 


29 


3.867 


32 


40 


46 


86130 


3.768 


56 


40 


28100 16 


3.818 


32 


64 


56 


72 


II 


3.868 


40 


56 


48 


86 14 


3.769 


46 


40 


32 


100 


II 


3.819 


40 


72 


64 


86 


22/2 


3.869 


56 


44 


28 


8621 


3.770 


48 


40 


32 


100 


II 


3.820 


56 


40 


28 


100 


13 


3,870 


32 


40 


44 


86 19 


3.771 


56 


44 


28 


86 


24/2 


3.821 


40 


64 


48 


72 


23/2 


3.871 


32 


44 


48 


8617/2 


3.772 


32 


44 


40 


72 


21 


3.822 


28 


40 


48 


86 


12 


3.872 


40 


72 


64 


8620/2 


3773 


44 


64 


48 


86 


10/2 


3.823 


28 


40 


48 


72 


35 


3.873 


56 


44 


28 


72 38/2 


3.774 


32 


64 


56 


72 


14 


3.824 


32 


64 


56 


72 


10 '/2 


3.874 


32 


44 


40 


721/6/2 


3.775 


48 


100 


56 


64 


26 


3.825 


44 


72 


f6 


86 


16 


3.875 


32 


48 


44 


72/8 


3.776 


48 


40 


32 


100 


10/2 


3.826 


32 


44 


48 


86 


19/2 


3.876 


40 


56 


48 


86 13/s. 


3.777 


40 


64 


48 


72 


25 


3.827 


56 


40 


28 


100 


12/2 


3.877 


40 


64 


48 


72 21/2 


3.778 


48 


72 


56 


86 


29 


3.828 


28 


40 


48 


86 


11/2 


3.878 


44 


72 


64 


8631/2 


3.779 


44 


64 


48 86 


10 


3.829 


56 


44 


28 


86 


22/2 


3.879 


32 


44 


56 


86 35 


3.780 


40 


56 


481 86 


18/2 


3.830 


40 


64 


56 


72 


38 


3.880 


32 


44 


56 


86 35 


3.781 


32 


64 


56 72 


13/2 


3.831 


44 


56 


4b 


72 


43 


3.881 


32 


40 


44 


86 18/2 


3.782 


48 


40 


32 


100 


10 


3.832 


40 


56 


48 


86 


16 


3.882 


56 


44 


28 


86 20/2 


3.783 


28 


40 


48 


86 


14/2 


3.833 


40 


72 


64 


66 


22 


3.883 


32 


44 


40 


72 16 


3.784 


44 


72 


56 


86 


18 


3.834 


56 


40 


28 


100 


12 


3.884 


40 


56 


48 


86 13 


3.785 


40 


48 


44 


72 


42 


3.835 


28 


40 


48 


86 


II 


3.885 


44 


72 


56 


86/2/2 


3.786 


56 


44 


28 


86 


24 


3.836 


40 


64 


48 


72 


23 


3.886 


56 


40 


28 


66 31/2 


3.787 


40 


64 


56 


86 


21/2 


3.837 


40 


64 


56 


86 


19 Vi 


3.887 


44 


64 


48 


72 32 


3.788 


32 


56 


64 


86 


27 


3.838 


32 


44 


48 


86 


19 


3.688 


48 


44 


40 


10027 


3.789 


32 


64 


56 


72 


13 


3.839 


86 


48 


24 


72 


50 


3.889 


40 


56 


44 


72 27 


3.790 


32 48 


44 


72 


21 Vz 


3.840 


32 


48 


44 


72 


19/2 


3.890 


40 


64 


48 


72 21 


3.791 


44100 


56 


64 


10 


3.841 


56 


40 


28 


100 


11% 


3.891 


40 


56 


48 


86- 12/2 


3.792 


40 64 


48 


72 


24& 


3.842 


56 


44 


28 


86 


22 


3.892 


44 


72 


56 


86 12 


3.793 


44 


72 


64 


86 


33 Vz 


3.843 


44 


72 


56 


86 


15 


3.893 


32 


44 


40 


72 15/z 


3.794 


32 


44 


48 


72 


38/2 


3.844 


56 


40 


28 


86 


32/ 2 


3.894 


56 


44 


28 


86 20 


3.795 


56 


40 


28 


100 


14/2 


3.845 


28 


44 


48 


72 


25 


3.895 


40 


48 


44 


86 24 


3.796 


32 


44 


40 


72 


20 


3.846 


28 


40 


48 


72 


34/2 


3.896 


32 


48 


44 


72117 


3.797 


32 


64 


56 


72 


12/2 


3.847 


32 


40 


4b 


86 


30/2 


3.897 


40 


72 


64 


66 19/2 


3.798 


48 


44 


40 


100 


29 Vz 


3.848 


28 


40 


48 


86 


10 


3.898 


56 


48 


24 


64127 


3.799 


28 


40 


48 


86 


13/2 


3.849 


32 


44 


48 


86 


18/2 


3.899 


44 


72 


56 


86 11/2 



A Treatise on Milling and Milling Machines 401 





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3.900 56 


44 


28 


72 


36 


3.950 


48 


72 


56 


86 


24/ 2 


4.000 


28 


40 


48 


72 


31 


3.901 56 


40 


32 


86 


4l'/z 


3.951 


48 


64 


56 


86 


36 


4001 


40 


48 


56 


86 


42/2 


3.902 


32 


44 


48 


86 


16 


3.952 


40 


64 


48 


72 


18/2 


4.002 


40 


64 


56 


86 


10/2 


3.903 


40 


64 


48 


72 


20/2 


3.953 


44 


64 


56 


86 


28 


4.003 


56 


44 


28 


86 


15 


3.904 


32 


40 


44 


86 


1 7/i 


3.954 


40 


48 


44 


86 


22 


4.004 


32 


40 


44 


86 


12 


3.905 


28 


44 


48 


72 


23 


3.955 


32 


44 


48 


86 


13 


4.005 


40 


64 


48 


72 


16 


3.906 


56 


44 


28 


86 


19/z 


3.956 


56 


40 


32 


100 


28 


4.006 


40 


64 


48 


72 


16 


3.907 


56 


40 


28 


86 


31 


3.957 


40 


64 


56 


86 


13/2 


4.007 


44 


64 


56 


86 


26/2 ' 


3.906 


44 


64 


48 


72 


31 /z 


3.958 


40 


64 


56 


86 


l3'/2 


4.008 


40 


64 


56 


86 


10 


3.909 


28 


48 


56 


72 


30 ft 


3.959 


32 


44 


40 


72 


11/2 


4.009 


56 


40 


32 


100 


26/l 


3.910 


56 


48 


28 


64 


40 


3.960 


28 


44 


48 


72 


21 


4.010 


56 


40 


32 


100 


26/2 


3.911 


32 


44 


48 


86 


15/2 


3.961 


32 


48 


44 


72 


13/2 


4.011 


32 


40 


44 


86 


lift 


3.912 


44 


72 


56 


86 


10 /i 


3.962 


32 


48 


44 


72 


13/2 


4.012 


56 


44 


28 


86 


l4/i 


3.913 


40 


56 


48 


86 


II 


3.963 


40 


64 


48 


72 


18 


4.013 


32 


40 


48 


86 


26 


3.914 


28 


40 


48 


72 


33 


3.964 


40 


72 


64 


86 


I6/2 


4.014 


48 


64 


32 


56 


20/2 


3.915 


48 


64 


32 


56 


24 


3.965 


56 


48 


24 


64 


25 


4.015 


40 


64 


48 


72 


15/2 


3.916 


40 


64 


48 


72 


20 


3.966 


32 


44 


40 


72 


II 


4.016 


32 


44 


56 


86 


32 


3.917 


56 


40 


28 


72 


44 


3.967 


56 


40 


28 


86 


29/a 


4.017 


48 


100 


56 


64 


17 


3.918 


56 


44 


28 


86 


19 


3.968 


28 


48 


56 


72 


29 


4.018 


32 


40 


44 


86 


II 


3.919 


44 


72 


56 


86 


10 


3.969 


44 


64 


48 


72 


30 


4.019 


40 


48 


44 


86 


19/2 


3.920 


32 


44 


40 


72 


14 


3.970 


32 


44 


48 


86 


12 


4.020 


40 


72 


64 


86 


13/2 


3.921 


32 


44 


48 


86 


15 


3.971 


44 


64 


58 


86 


27'A 


4.021 


56 


44 


28 


86 


14 


3.922 


40 


64 


56 


86 


15/2 


3.972 


32 


44 


40 


72 


10/2 


4.022 


56 


48 


28 


64 


38 


3.923 


40 


56 


44 


72 


26 


3.973 


56 


44 


28 


86 


16/2 


4.023 


28 


44 


48 


72 


18/2 


3.924 


32 


40 


44 


86 


16/2 


3.974 


40 


64 


48 


72 


17/2 


4.024 


56 


40 


28 


86 


28 


3.925 


40 


56 


48 


86 


10 


3.975 


32 


56 


64 


72 


38/2 


4.025 


40 


64 


48 


72 


15 


3.926 


32 


44 


56 


86 


34 


3.976 


48 


64 


56 


86 


35/2 


4.026 


56 


44 


24 


64 


32'/2 


3.927 


56 


40 


28 


86 


30/2 


3.977 


32 


44 


48 


86 


ir/2 


4.027 


56 


40 


32 


100 


26 


3.928 


40 


64 


48 


72 


J9/2 


3.978 


32 


44 


48 


86 


11/2 


4.028 


44 


64 


48 


72 


28/2 


3.929 


44 


64 


48 


72 


31 


3.979 


32 


44 


40 


72 


10 


4,029 


56 


44 


28 


86 


13/2 


3.930 


56 


44 


28 


86 


18/2 


3.980 


32 


40 


44 


86 


13/2 


4.03O 


32 


40 


46 


86 


25/2 


3.931 


40 


64 


56 


86 


15 


3.981 


40 


64 


56 


86 


12 


4.031 


32 


40 


44 


86 


10 


3.932 


40 


72 


64 


86 


18 


3.982 


40 


64 


56 


72 


35 


4.032 


32 


56 


64 


86 


16/2 


3.93^ 


26 


44 


48 


72 


22 


3.983 


56 


44 


28 


86 


16 


4.033 


40 


56 


44 


72 


22/2 


3.934 


32 


40 


44 


86 


16 


3.984 


32 


44 


48 


86 


11 


4.034 


40 


64 


48 


72 


14/2 


3.935 


32 


48 


44 


72 


15 


3.985 


40 


64 


48 


72 


17 


4.035 


44 


64 


56 


72 


41 


3.936 


32 


44 


40 


72 


13 


3.986 


56 


40 


28 


86 


29 


4.036 


40 


72 


64 


86 


12/2 


3.937 


56 


40 


32 


100 


28/i 


3.987 


56 


40 


28 


86 


29 


4.037 


48 


100 


56 


64 


16 


3.938 


32 


44 


48 


86 


14 


3.988 


40 


64 


56 


86 


lift 


4.038 


56 


44 


28 


86 


13 


3.939 


44 


72 


64 


86 


30 


3.989 


44 


64 


48 


72 


29/2 


4.039 


48 


72 


56 


86 


ZVh 


3.940 


40 


64 


48 


72 


19 


3.990 


44 


56 


48 


86 


24/2 


4.040 


48 


64 


32 


56 


19/2 


3.941 


56 


44 


28 


86 


18 


3.991 


32 


44 


48 


86 


10/2 


4.041 


44 


64 


56 


86. 


25/2 


3.942 


32 


56 


64 


86 


22 


3.992! 56 


40 


32 


100 


27 


4.042 


28 


40 


48 


72 


30 


3.943 


40 


72 


64 


86 


17/2 


3.993 


56 


44 


28 


86 


15/2 


4.043 


40 


64 


48 


72 


14 


3.944 


32 


44 


40 


72 


12/2 


3.994 


32 44 


56 


86 


32/2 


4.044 


56 


40 


32 


100 


25/2 


3.945 


48 


64 


32 


56 


23 


3.995 


40 64 


48 


72 


16/2 


4.045 


56 


48 


44 


100 


38 


3.946 


48 


64 


32 


56 


23 


3.996 


32|40 


44 


86 


\Z'/z 


4.046 


56 


44 


28 


86 


IZ/2 


3.947 


32 


44 


48 


86 13/2 


3.997 


32 1 44 


48 


86 


10 


4.047 


44 


64 


48 


72 


28 


3.948 


40 


56 


48 


72 


34 


3.998 


40 44 


48 


86 


38 


4.048 


56 


44 24 


64 


32 


3.949 


40 


64 


56 


86 


14 


3.999 


32|48 


44 


72 


II 


4.049 


48 


64 56 


86 


34 



402 



The Cincinnati Milling Machine Company 





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4.050 


40 


72 


64 


86 


II 72 


4.100 


48 


100 


56 


64 


l2'/z 


4.150 


48 


64 


32 


56 


14/2 


4.051 


40 


72 


64 


66 


N'/i 


4.101 


32 


44 


56 


86 


30 


4.151 


44 


64 


56 


66 


22 


4.052 


40 


64 


48 


72 


13/z 


4.102 


28 


40 


48 


72 


2eV/a 


4.152 


56 


48 


44 


100 


36 


4. 05$ 


56 


44 


28 


86 


12 


4.103 


56 


44 


28 


72 


34 


4.153 


56 


48 


44 


100 


36 


4.054 


40 


64 


56 


72 


33'/i 


4.104 


48 


72 


56 


86 


19 


4.154 


44 


64 


48 


72 


25 


4.055 


40 


48 


44 


86 


\e> 


4.105 


44 


72 


64 


86 


25/2 


4.155 


44 


72 


64 


86 


24 


4.Q56 


56 


48 


24 


64 


22 


4.106 


44 


64 


56 


86 


23 Vz 


4.156 


32 


44 


48 


1Z 


31 


4.057 


46 


100 


56 


64 


15 


4.107 


28 


44 


48 


72 


14/2 


4.157 


28 


44 


48 


72 


ll'/i 


4.058 


44 


64 


56 


86 


25 


4.108 


56 


40 


32 


100 


23fe 


4.158 


28 


40 


48 


72 


27 


4.059 


32 


44 


56 


86 


31 


4.109 


56 


40 


32 


100 


?3'/2 


4.159 


32 


56 


64 


66 


(2 


4.060 


40 


64 


48 


72 


13 


4.110 


48 


64 


32 


56 


16'/* 


4.160 


56 


40 


32 


86 


37 


4.061 


56 


44 


28 


86 


life 


4,111 


56 


48 


24 


64 


20 


4.161 


28 


48 


56 


72 


23/2 


4.062 


28 


40 


48 


72 


29/2 


4.112 


28 


48 


56 


72 


25 


4.162 


32 


44 


56 


86 


28/2 


4.063 


32 


40 


48 


86 


24 Vz 


4.113 


56 


44 


24 


64 


30 fe 


4.163 


40 


48 


44 


86 


12/2 


4. 0*4 


48 


64 


32 


56 


I8/2 


4.114 


56 


40 


28 


86 


25 Vz 


4.164 


56 


40 


28 


86 


24 


4.065 


44 


64 


48 


72 


27 Vz 


4.115 


40 


56 


44 


72 


19/2 


4.165 


44 


64 


56 


86 


21/2 


4.066 


48 


100 


56 


64 


l4/i 


4.116 


48 


100 


56 


64 


\\Vz 


4.166 


44 


64 


56 


86 


2l'/z 


4.067 


28 


44 


48 


72 


16/2 


4.117 


32 


56 


64 


86 


14/2 


4.167 


32 


56 


64 


86 


11/2 


4.068 


40 


64 


48 


72 


life 


4.116 


86 


64 


26 


72 


38 


4.166 


56 


40 


32 


100 


21/2 


4.069 


32 


44 


56 


72 


44 


4.119 


44 


64 


46 


72 


26 


4.169 


32 


40 


48 


86 


21 


4.070 


44 


72 


64 


86 


26/2 


4.120 


48 


64 


32 


56 


16 


4.170 


44 


64 


48 


72 


24/2 


4.071 


40 


72 


64 


86 


10 


4.121 


28 


40 


48 


72 


28 


4.171 


44 


72 


64 


86 


23/2 


4.072 


56 


48 


44 


100 


37'/* 


4.122 


32 


44 


56 


86 


29/2 


4.172 


56 


48 


24 


64 


17/2 


4.073 


48 


64 


56 


86 


33/2 


4.123 


48 


100 


56 


64 


11 


4.173 


48 


72 


56 


86 


16 


4.074 


44 


64 


56 


86 


24/2 


4.124 


56 


40 


32 


too 


23 


4.174 


32 


56 


64 


86 


II 


4.075 


56 


44 


28 


86 


10/2 


4.125 


28 


44 


48 


72 


IB'/i 


4.175 


56 


44 


24 


64 


29 


4.076 


40 


64 


46 


72 


12 


4.126 


32 


56 


64 


86 


14 


4.176 


28 


56 


64 


72 


20 


4.077 


56 


40 


32 


100 


24 Vz 


4.127 


40 


56 


44 


72 


19 


4.177 


28 


40 


48 


72 


26/2 


4.078 


28 


46 


56 


72 


26 


4.128 


28 


46 


56 


72 


24/i 


4.176 


28 


44 


46 


72 


10 


4.079 


56 


40 


28 


86 


26'/* 


4.129 


28 


48 


56 


72 


24/2 


4.179 


56 


48 


44 


100 


35/2 


4.080 


44 


56 


48 


86 


2l/i 


4.130 


48 


100 


56 


64 


10/2 


4.160 


56 


40 


28 


66 


23/i 


4.081 


56 


44 


28 


86 


10 


4.131 


56 


40 


28 


86 


25 


4.181 


32 


56 


64 


86 


10/2 


4.082 


28 


40 


48 


72 


29 


4.132 


72 


56 


24 


64 


31 


4.182 


32 


44 


56 


86 


28 


4.083 


40 


64 


48 


72 


ll/i 


4.133 


26 


44 


48 


72 


13 


4.183 


56 


40 


32 


100 


21 


4.084 


44 


64 


48 


72 


27 


4.134 


32 


56 


64 


86 


l3/i 


4.164 


48 


64 


32 


56 


12/2 


4.085 


56 


48 


24 


64 


21 


4.135 


32 


56 


64 


86 


13/2 


4.185 


40 


56 


44 


72 


16/2 


4.086 


32 


48 


56 


72 


38 


4.136 


44 


64 


56 


86 


22'/i 


4.166 


44 


72 


64 


86 


23 


4.087 


32 


56 


64 


86 


16 


4.137 


44 


64 


48 


72 


25'/2 


4.187 


44 


64 


48 


72 


24 


4.088 


44 


72 


64 


86 


26 


4.138 


44 


72 


64 


86 


24 Vz 


4.188 


40 


64 


56 


72 


30 '/a 


4.089 


40 


46 


44 


66 


16/2 


4.139 


44 


72 


64 


86 


Z4/2 


4.169 


26 


56 


64 


72 


19/2 


4.090 


40 


64 


46 


72 


II 


4.140 


26 


40 


48 


72 


27/2 


4.190 


64 


46 


32 


72 


45 


4.091 


40 


64 


48 


72 


II 


4.141 


28 


44 


48 


72 


I2V2 


4.191 


32 


40 


44 


72 


31 


4.092 


48 


100 


56 


64 


13 


4.142 


32 


44 


56 


86 


29 


4.192 


28 


48 


56 


72 


22/z 


4.093 


56 


40 


32 


100 


24 


4.143 


32 


56 


64 


86 


13 


4.193 


44 


64 


56 


86 


20/2 


4.094 


44 


56 


46 


86 


21 


4.144 


32 


40 


46 


72 


39 


4.194 


44 


64 


56 


86 


20/2 


4.095 


28 


48 


56 


72 


25ft 


4.145 


26 


48 


56 


72 


24 


4.195 


28 


40 


48 


72 


26 


4.096 


48 


64 


56 


86 


33 


4.146 


40 


48 


44 


86 


l3'/2 


4.196 


56 


40 


28 


86 


23 


4.097 


40 


64 


46 


72 


IO'/l 


4.147 


56 


40 


26 


66 


24/i 


4.197 


56 


44 


28 


72 


3Z 


4.098 


56 


48 


24 


64 


20'/i 


4.148 


56 


40 


28 


66 


24/2 


4.198 


32 


44 


28 


72 


30 


4.099 


40 


46 


44 


86 


16 


4.149 


28 


44 


48 


71 


12 


4.199 


40 


46 


44 


86 


10 



A Treatise on Milling and Milling Machines 403 





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4.200 


46 


64 


32 


56 


lift 


4.250 


28 


48 


56 


72 


20 '/i 


4.300 


44 


72 


64 


86 


19 


4.201 


32 


44 


56 


86 


27/x 


4251 


40 


64 


56 


72 


29 


4.301 


56 


72 


64 


86 


42 


4.202 


44 


72 


64 


86 


22 Vx 


4.252 


48 


44 


40 


100 


13 


4.302 


28 


48 


56 


72 


18/2 


4.203 


44 


64 


46 


72 


ZVh 


4.253 


40 


56 


44 


72 


13 


4303 


32 


40 


46 


86 


15/2 


4.204 


44 


56 


48 


86 


16/2 


4.254 


48 


72 


56 


86 


It/2 


4304 


44 


64 


56 


86 


16 


4.205 


48 


44 


40 


100 


l5/i 


4.255 


56 


40 


28 


66 


21 


4.305 


44 


56 


48 


86 


II 


4.206 


40 


56 


44 


72 


15/2 


4256 


40 


44 


48 


86 


33 


4.306 


56 


40 


32 


100 


16 


4.207 


28 


48 


56 


72 


22 


4.257 


32 


44 


56 


86 


26 


4.307 


44 


64 


48 


72 


20 


4.208 


48 


64 


56 


86 


30/2 


4.258 


44 


64 


56 


86 


18 


4.308 


56 


48 


24 


64 


10 


4.209 


32 


40 


48 


86 


19/2 


4.259 


32 


40 


48 


72 


37 


4.309 


32 


44 


56 


86 


24/2 


4.2 10 


56 


40 


32 


100 


20 


4.260 


44 


72 


64 


86 


20/2 


4.310 


32 


44 


56 


86 


24/2 


4.211 


56 


40 


28 


86 


22'/2 


4.261 


56 


40 


32 


100 


18 


4.311 


44 


56 


64 


86 


42/2 


4.212 


28 


40 


48 


72 


25'/2 


4.262 


40 


56 


48 


72 


26'/2 


4.312 


28 


40 


46 


72 


22/2 


4.213 


32 


40 


44 


72 


30/2 


4.263 


28 


40 


48 


72 


24 


4.313 


44 


72 


64 


86 


16/2 


4.214 


48 


64 


32 


56 


IO'/2 


4264 


28 


40 


48 


72 


24 


4.314 


44 


64 


56 


86 


15/2 


4.215 


48 


44 


40 


100 


15 


4265 


56 


44 


28 


64 


40 


4315 


28 


48 


56 


72 


18 


4.216 


40 


56 


44 


72 


15 


4.266 


48 


64 


56 


72 


43 


4.316 


40 


56 


48 


72 


25 


4.217 


44 


72 


64 


86 


22 


4.267 


56 


40 


32 


86 


35 


4.317 


56 


40 


32 


100 


15/2 


4.216 


40 


56 


64 


86 


37/a 


4.268 


48 


72 


56 


86 


10/2 


4.318 


44 


56 


46 


86 


10 


4.219 


44 


64 


48 


72 


23 


4.269 


56 


40 


28 


86 


20/a 


4.319 


40 


48 


44 


72 


32 


4.220 


32 


44 


56 


86 


27 


4.270 


44 


64 


56 


86 


17/2 


4.320 


44 


64 


48 


72 


19/2 


4.221 


28 


48 


56 


72 


21/2 


4.271 


56 


48 


24 


64 


12/2 


4.321 


28 


56 


64 


72 


13/2 


4.222 


40 


46 


44 


72 


34 


4.272 


26 


56 


64 


72 


16 


4.322 


56 


40 


28 


86 


18/2 


4.223 


56 


40 


32 


100 


19/2 


4.273 


56 


40 


32 


100 


17/2 


4.323 


56 


40 


28 


86 


18/2 


4.224 


40 


56 


48 


72 


27/2 


4.274 


44 


72 


64 


86 


20 


4.324 


44 


64 


56 


86 


15 


4.225 


48 


44 


40 


100 


14/2 


4.275 


32 


44 


56 


86 


25/2 


4.325 


44 


72 


64 


86 


18 


4.226 


56 


40 


28 


86 


22 


4.276 


48 


44 


40 


100 


ll/z 


4.326 


32 


44 


56 


86 


24 


4.227 


28 


56 


64 


72 


18 


4.277 


28 


48 


56 


72 


19/2 


4.327 


32 


44 


56 


86 


24 


4.228 


86 


64 


28 


72 


36 


4.278 


46 


64 


40 


56 


37 


4.328 


56 


44 


28 


72 


29 


4.229 


40 


56 


64 


86 


35/2 


4.279 


44 


64 


48 


72 


21 


4.329 


56 


44 


28 


72 


29 


4.230 


28 


40 


48 


72 


25 


4.280 


28 


40 


48 


72 


23'/a 


4.330 


28 


56 


64 


72 


13 


4.231 


44 


72 


64 


86 


21/2 


4.281 


44 


64 


56 


86 


17 


4.331 


40 


64 


56 


72 


27 


4.232 


44 


72 


64 


86 


21/2 


4.282 


28 


56 


64 


72 


15/2 


4.332 


32 


40 


48 


86 


14 


4.233 


56 


72 


64 


86 


43 


4.283 


56 


40 


28 


86 


20 


4.333 


44 


64 


46 


72 


19 


4.234 


48 


44 


40 


100 


14 


4.284 


56 


40 


32 


too 


17 


4.334 


44 


64 


56 


86 


14/2 


4.235 


40 


56 


44 


72 


14 


4.285 


40 


56 


44 


72 


II 


4.335 


56 


40 


28 


86 


18 


4.236 


28 


48 


56 


72 


2! 


4.286 


56 


44 


28 


72 


30 


4.336 


32 


40 


44 


72 


27/i 


4.237 


72 


56 


24 


64 


28/2 


4.287 


44 


72 


64 


86 


19/2 


4.337 


44 


72 


64 


86 


17/2 


4.23b 


32 


44 


56 


86 


26/2 


4.288 


44 


72 


64 


86 


19/2 


4.338 


44 


72 


64 


86 


17/2 


4.239 


48 


64 


44 


56 


44 


4.289 


44 


56 


48 


86 


12 


4.339 


28 


48 


56 


72 


17 


4.240 


32 


44 


48 


72 


29 


4290 


26 


48 


56 


72 


19 


4.340 


72 


48 


24 


64 


39/2 


4.241 


56 


40 


28 


86 


21/2 


4.291 


48 


44 


40 


too 


10/2 


4.341 


86 


56 


24 


72 


32 


4.242 


56 


44 


28 


72 


31 


4.292 


32 


44 


56 


86 


25 


4.342 


28 


40 


46 


72 


21/2 


4.243 


48 


44 


40 


100 


13/2 


4293 


44 


64 


48 


72 


20/2 


4.343 


32 


44 


56 


86 


23/2 


4.244 


40 


56 


44 


72 


13/2 


4.294 


64 


44 


32 


86 


37/2 


4.344 


44 


64 


56 


86 


14 


4.245 


56 


48 


24 


64 


14 


4.295 


56 


48 


24 


64 


II 


4.345 


64 


46 


24 


56 


40/z 


4.246 


44 


72 


64 


86 


21 


4.296 


28 


40 


48 


72 


23 


4.346 


44 


64 


48 


72 


18/2 


4.247 


26 


40 


48 


72 


24/2 


4.297 


56 


40 


28 


86 


19/2 


4.347 


56 


40 


28 


86 


17/2 


4.246 


56 


40 


32 


100 


18/2 


4298 


48 


44 


40 


100 


10 


4.348 


32 


48 


56 


72 


33 


4.249 


44 


64 


46 


72 


22 


4.299 


40 


56 


44 


72 


10 


4.349 


44 


72 


64 


86 


17 



404 



The Cincinnati Milling Machine Company 





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4.350 


28 


48 


56 


72 


16 ft 


4.400 


40 


56 


48 


72 


22 ft 


4.450 


32 


44 


56 


86 


20 


4.351 


32 


40 


48 


86 


13 


4.401 


44 


48 


56 


86 


42 ft 


4.451 


28 


40 


48 


72 


17ft 


4.352 


56 


48 


28 


64 


31 ft 


4.402 


28 


48 


56 


72 


14 


4.452 


44 


64 


56 


86 


6 


4.35 3 


44 


64 


56 


86 


13ft 


4.403 


56 


40 


28 


86 


15 


4.453 


28 


48 


56 


72 


II 


4.354 


32 


56 


64 


72 


31 


4.404 


64 


48 


32 


72 


42 


4.454 


28 


48 


56 


72 


II 


4.355 


28 


56 


64 


72 


lift 


4.405 


44 


64 


48 


72 


16 


4.455 


86 


56 


24 


72 


29ft 


4.356 


56 


40 


32 


100 


13'/* 


4.406 


32 


44 


56 


86 


21ft 


4.456 


44 


64 


48 


72 


13ft 


4.357 


28 


40 


48 


72 


21 


4.407 


32 


44 


56 


86 


21ft 


4.457 


44 


72 


64 


86 


lift 


4.358 


86 


64 


28 


72 


33ft 


4.408 


48 


64 


56 


86 


25 ft 


4.458 


56 


40 


28 


86 


12 


4.359 


32 


44 


56 


86 


23 


4.409 


44 


64 


56 


86 


10 


4.459 


64 


40 


32 


86 


41ft. 


4.360 


32 


44 


56 


86 


23 


4.410 


56 


44 


24 


64 


22ft 


4.460 


40 


56 


48 


72 


20 ft 


4.361 


44 


72 


64 


86 


16ft. 


4.411 


32 


44 


48 


72 


24 ft 


4.461 


28 


48 


56 


72 


10ft 


4.362 


44 


64 


56 


86 


13 


4.412 


28 


48 


56 


72 


13ft 


4.462 


48 


64 


56 


86 


24 


4.363 


28 


56 


64 


72 


II 


4.413 


28 


40 


48 


72 


19 


4.463 


28 


40 


48 


72 


17 


4.364 


40 


44 


56 


86 


42ft 


4.414 


48 


64 


44 


56 


41ft 


4.464 


32 


44 


56 


86 


19 ft 


4.365 


56 


40 


32 


100 


13 


4.415 


40 


56 


48 


72 


22 


4.465 


44 


64 


48 


72 


13 


4.366 


40 


48 


44 


72 


31 


4.416 


44 


64 


48 


72 


15ft 


4.466 


44 


64 


48 


72 


13 


4.367 


32 


40 


48 


86 


12 


4.417 


56 


40 


32 


86 


32 


4.467 


56 


44 


28 


72 


25ft 


4.368 


44 


56 


48 


72 


33ft 


4416 


44 


56 


48 


72 


32ft 


4.468 


28 


48 


56 


72 


10 


4.369 


72 


56 


24 


64 


25 


4.419 


56 


40 


32 


100 


9'/2 


4.469 


40 


44 


48 


72 


42ft 


4.370 


56 


40 


28 


86 


16 ft 


4.420 


48 


72 


64 


86 


27 


4.470 


44 


48 


56 


86 


41ft 


4.371 


28 


40 


48 


72 


20 ft 


4.421 


32 


44 


56 


86 


21 


4.471 


44 


48 


56 


86 


41ft 


4.372 


28 


40 


48 


72 


20 ft 


4.422 


56 


40 


28 


86 


14 


4.472 


44 


72 


64 


86 


10 ft 


4.373 


32 


48 


56 


72 


32 ft 


4423 


56 


40 


28 


86 


14 


4.473 


86 


48 


24 


72 


41ft 


4.374 


56 


40 


32 


100 


12ft 


4.424 


40 


48 


64 


86 


44ft 


4.474 


44 


64 


48 


72 


12 ft 


4.375 


32 


44 


56 


86 


22 ft 


4.425 


64 


40 


32 


86 


42 


4.475 


28 


40 


48 


72 


16ft 


4.376 


32 


44 


56 


86 


22ft 


4.426 


28 


40 


48 


72 


18ft 


4.476 


40 


48 


44 


72 


28 ft 


4.377 


56 


44 


24 


64 


23ft 


4.427 


44 


64 


48 


72 


15 


4.477 


86 


56 


24 


72 


29 


4.378 


64 


44 


32 


86 


36 


4.428 


32 


44 


56 


72 


38ft 


4.478 


32 


44 


56 


86 


19 


4.379 


44 


64 


56 


86 


12 


4.429 


28 


48 


56 


72 


12ft 


4.479 


44 


72 


64 


86 


10 


4.380 


48 


72 


64 


86 


28 


4.430 


28 


48 


56 


72 


12 ft 


4.480 


40 


44 


48 


86 


28 


4.381 


56 


40 


28 


86 


16 


4.431 


44 


72 


64 


86 


13 


4.481 


48 


64 


44 


56 


40ft 


4.382 


28 


48 


56 


72 


15 


4.432 


56 


40 


28 


86 


13ft 


4.482 


56 


40 


28 


86 


10 ft 


4.383 


44 


64 


48 


72 


17 


4.433 


40 


48 


44 


72 


29ft 


4.483 


44 


64 


48 


72 


12 


4.384 


40 


56 


48 


72 


23 


4.434 


40 


44 


56 


86 


41ft 


4.484 


32 


40 


44 


72 


23ft 


4.385 


40 


48 


64 


86 


45 


4.435 


48 


64 


56 


72 


40 ft 


4.485 


56 


44 


28 


72 


25 


4.386 


28 


40 


48 


72 


20 


4.436 


32 


44 


56 


86 


20ft 


4.486 


28 


40 


48 


72 


16 


4.387 


44 


64 


56 


86 


lift 


4.437 


44 


64 


48 


72 


14ft 


4.487 


64 


44 


32 


86 


34 


4.388 


48 


64 


40 


56 


35 


4.438 


28 


48 


56 


72 


12 


4.488 


56 


40 


32 


86 


30 ft 


4.389 


64 


40 


sa 


86 


42ft 


4.439 


28 


40 


48 


72 


18 


4.489 


56 


40 


28 


86 


10 


4.390 


56 


40 


32 


100 


life 


4.440 


44 


72 


64 


86 


12 ft 


4.490 


32 


48 


56 


72 


30 


4.391 


32 


44 


56 


86 


22 


4.441 


56 


40 


28 


86 


13 


4.491 


32 


44 


56 


86 


18ft 


4.392 


56 


40 


28 


86 


15ft 


4.442 


56 


48 


28 


64 


29 ft 


4492 


72 


48 


24 


64 


37 


4.393 


44 


72 


64 


86 


15 


4.443 


32 


56 


64 


72 


29 


4.493 


64 


40 


32 


86 


41 


4.394 


44 


64 


48 


72 


16 'ft 


4.444 


48 


64 


56 


86 


24 ft 


4.494 


64 


40 


32 


86 


41 


4.395 


44 


64 


56 


86 


II 


4.445 


56 


48 


44 


100 


30 


4.495 


32 


44 


48 


72 


22 


4.396 


32 


44 


56 


72 


39 


4.446 


28 


48 


56 


72 


lift 


4.496 


48 


64 


56 


86 


23 


4.397 


32 


40 


48 


86 


10 


4.447 


44 


64 


48 


72 


14 


4.497 


28 


40 


48 


72 


15ft 


4.398 


56 


40 


32 


100 


11 


4.448 


48 


64 


44 


56 


41 


4.498 


56 


72 


64 


86 


39 


4.399 


28 


40 


48 


72 19/2 


4.449 


44 


72 


64 


86 


12 


4.499 


56 


44 


24 


64 


19 ft 



A Treatise on Milling and Milling Machines 405 





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4.500 56 44 32 64 45 


4.550 


48 


72 


64 


86 


23/z 


4.600 


40 


56 


48 


72 


15 


4.501 4ft 64 56 72 39 'A 


4.551 


72 


48 


24 


64 


36 


4.601 


40 


44 


56 


86 


39 


4.502 40 44 56 86 40/i 


4.552 


32 


44 


56 


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16 


4.602 


40 


48 


56 


86 


32 


4.503 64 48 Z4 56 38 


4553 


32 


44 


56 


86 


16 


4.603 


44 


56 


48 


72 


28/i 


4.504 32 44 56 86 18 


4.554 


40 


56 


48 


72 


17 


4.604 


48 


64 


56 


86 


19 /a 


4.505 56 44 28 64 36 


4,555 


56 


44 


lb 


72 


23 


4.605 


32 


44 


56 


86 


13/2 


4.506 44 64 48 72 10/2 


4.556 


28 


40 


48 


72 


12/2 


4.606 


44 


48 


56 


86 


39 /a 


4.507 1 86| 48 24 72 41 


4.557 


32 


48 


56 


72 


28/2 


4.607 


44 


56 


64 


86 


38 


4.508 ! 28 40 48 72 15 


4.558 


72 


56 


24 


64 


19 


4.608 


86 


48 


24 


72 


39/a 


4.503! 44i 64 56 72 32 Vi 


4.559 


44 


56 


48 


72 


29/2 


4.609 


32 


40 


44 


72 


l9'/2 


4.510 


44 64 56 72 32 % h 


4.560 


48 


64 


56 


86 


2! 


4.610 


40 


56 


48 


72 


14/2 


4.511 


32 44 48 72 21/z 


4.56 i 


64 


40 


32 


86 


40 


4.611 


32 


44 


48 


72 


18 


4.512 


44| 56 64 86 39/2 


4.562 


44 


40 


48 


86 


42 


4.612 


48 


64 


44 


56 


38/2 


4.513 


44| 64 48 72 10 


4.563 


64 


48 


24 


56 


37 


4.613 


56 


48 


44 


100 


26 


4.514 


48 64 44 


56 40 


4.564 


32 


44 


56 


86 


15/2 


4.614 


32 


44 


56 


86 


13 


4.515 


48 


64 


44 


56:40 


4.565 


28 


40 


48 


72 


12 


4.615 


32 


44 


56 


86 


13 


4.516 


40 


56 


48 


72 18/2 


4.566 


40 


56 


48 


72 


16/2 


4.616 


48 


72 


64 


86 


21/2 


4.517 


32 


44 


56 


86 17/2 


4.567 


48 


72 


64 


86 


23 


4.617 


40 


44 


48 


86 


24/2 


4.518 


28 


40 


48 


72 j 14/2 


4.568 


40 


44 


56 


86 


39/2 


4.618 


48 


64 


56 


86 


19 


4.519 


28 


40 


48 


72! 14/2 


4.569 


86 


56 


24 


64 


37/2 


4.619 


32 


40 


48 


72 


30 


4.520 


86 


56i 24 


7228 


4570 


32 


44 


48 


72 


19/2 


4.620 


40 


56 


48 


72 


14 


4.521 


56 


441 28 


72 24 


4.57! 


86 


64 


28 


72 


29 


4.621 


40 


56 


48 


72 


14 


4.522 


72 


48 24; 64i36'/i 


4.572 


44 


48 


56 


86 


40 


4.622 


56 


72 


64 


86 


37 


4.523 


40 


64| 56 72 21/a 


4.573 


28 


40 


48 


72 


11/2 


4.623 


56 


72 


64 


86 


37 


4.524 


72 


44 24 64 42/2 


4.574 


32 


44 


56 


86 


15 


4624 


32 


44 


56 


86 


12/2 


4.525 


40 


48 56 86 33/2 


4.575 


32 


44 


56 


86 


15 


4.625 


44 


56 


48 


72 


26 


4.526 


56 44 


24 


64 I8/2 


4.576 


44 


56 


64 


66 


38/2 


4.626 


56 


48 


28 


64 


25 


4.527 


64 


40 


32 


86 40/s 


4.577 


32 


44 


56 


72 


36 


4.627 


64 


40 


32 


86 


39 


4.528 


28 


40 


48 


72 


14 


4.578 


40 


56 


46 


72 


16 


4,628 


48 


64 


56 


72 


37/2 


4.529 


32 


44 


56 


86 


17 


4.579 


72 


48 


24 


64 


35/2 


4.629 


86 


56 


24 


64 


36/a 


4.530 


56 


72 


64 


86 


38/2 


4.580 


48 


64 


44 


56 


39 


4.630 


86 


56 


24 


64 


36/2 


4.531 


64 


44 


32 


72 


45/2 


4.581 


28 


40 


48 


72 


II 


4.631 


40 


56 


48 


72 


13/2 


4.532 


48 


72 


64 


86 


24 


4.582 


40 


64 


56 


72 


19/2 


4.632 


32 


44 


56 


86 


12 


4.533 


48 


64 


56 


72 


39 


4.583 


48 


72 


64 


86 22/2 


4.633 


32 


44 


56 


86 


12 


4.534 


56 


40 32 


86 


29/2 


4.584 


32 


44 


48 


72 19 


4.634 


32 


44 


56 


72 


35 


4.535 


40 


44 56 


86 


40 


4.585 


32 


44 


56 


66 


14/2 


4.635 


40 


44 


48 


86 


24 


4.536 


44 


56 48 


72 


30 


4.586 


72 


56 


32 


64 


44/a 


4.636 


72 


48 


24 


64 


34/2 


4.537 


44 


56 


48 


72 


30 


4.587 


56 


48 


28 


64 


26 


4.637 


64 


48 


32 


72 


38/2 


4.538 


28 


40 


48 


72 


I3V2 


4.588 


56 


44 


24 


64 16 


4.638 


64 


48 


32 


72 


38/2 


4.539 


44 


48 


56 


86 


40/2 


4.589 


26 


40 


48 


72 


10/2 


4.639 


44 


48 


56 


86 


39 


4.540 


64 


48 


32 


72 


40 


4.590 


46 


64 


56 


86 


20 


4.640 


40 


56 


48 


72 


13 


4.541 


32 


44 


56 


86 


16/2 


4.591 


56 


40 


28 


72 


32/2 


4.641 


32 


44 


56 


66 


M/2 


4.542 


40 


56 


48 


72 


17/2 


4.592 


56 


72 


64 


86 


37/2 


4.642 


32 


40 


48 


72 


29/2 


4.543 


48 


64 


40 


56 


32 


4.593 


64 


48 


24 


56 


36/2 


4643 


40 


44 


48 


72 


40 


4.544 


44 


56 


64 


86 


39 


4.594 


64 


40 


32 


66 


39/2 


4.644 


48 


64 


44 


56 


36 


4.545 


72 


56 24 


64 


19/2 


4.595 


32 


44 


56 


86 14 


4.645 


48 


64 


56 


86 


16 


4.546 


32 


56! 64 


7226/2 


4.596 


28 


40 


48 


72 


10 


4.646 


72 


56 


24 


64 


15/2 


4.547 


28 


40 48 


72! 13 


4.597 


48 


64 


56 


72 


38 


4.647 


48 


72 


64 


86 


20 h 


4.548 


32 


44 


56 


72 


36/2 


4.598 


72 


56 


24 


64 


17/2 


4.648 


32 


44 


48 


72 


16/2 


4.549 


32 


40 


44 


72 


21/2 


4.599 


86 


56 


24 


64 


37 


4.649 


32 


44 


56 


86 


II 



406 



The Cincinnati Milling Machine Company 





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4.650 


32 


40 


44 


72 


\b 


4.700 


44 


56 


64 


86 


36 fe 


4.750 


32 


44 


48 


72 


life 


4.651 


56 


44 


24 


64 


13 


4.701 


64 


48 


32 


72 


37 fe 


4.751 


32 


44 


48 


72 


life 


4.652 


64 


48 


24 


56 


35V* 


4.702 


64 


48 


32 


72 


37fe 


4.752 


32 


40 


48 


72 


27 


4653 


56 


72 


64 


86 


36 fe 


4.703 


44 


40 


48 


86 


40 


4.753 


40 


44 


48 


86 


20 fe 


4.654 


44 


64 


56 


72 


29 fe 


4.704 


44 


48 


56 


86 


38 


4.754 


32 


40 


44 


72 


I3fe 


4.655 


56 


44 


32 


64 


43 


4,705 


48 


72 


64 


86 


I8fe 


4.755 


64 


40 


32 


86 


37 


4.656 


86 


64 


28 


72 


27 


4.706 


86 


48 


24 


72 


38 


4.756 


86 


64 


28 


72 


24 fe 


4.657 


32 


44 


56 


86 


lOfe 


4.707 


48 


64 


44 


56 


37 


4.757 


56 


44 


28 


72 


16 


4.656 


48 


64 


56 


72 


37 


4.708 


44 


56 


46 


72 


26 


4.758 


32 


56 


64 


72 


20fe 


4.659 


48 


64 


56 


72 


37 


4.709 


64 


48 


24 


56 


34fe 


4.759 


40 


44 


56 


86 


36 fe 


4.660 


64 


40 


32 


86 


38'/» 


4.710 


32 


56 


64 


72 


22 


4.760 


44 


56 


64 


86 


35 fe 


4.661 


40 


64 


56 


72 


16 fe 


4.711 


32 


40 


44 


72 


I5fe 


4.761 


56 


40 


28 


72 


29 


4.662 


32 


44 


56 


72 


34/* 


4.712 


56 


72 


64 


86 


35fe 


4762 


56 


40 


28 


72 


29 i 


4.663 


72 


48 


24 


64 


34 


4.713 


56 


44 


48 


100 


39 fe 


4.763 


40 


64 


56 


72 


life 


4.664 


32 


44 


56 


86 


10 


4.714 


32 


44 


48 


72 


I3fe 


4.764 


64 


48 


32 


72 


36fe 


4.665 


40 


44 


56 


86 


38 


4.715 


56 


48 


28 


64 


22 fe 


4.765 


64 


48 


24 


56 


33 fe 


4.666 


40 


56 


48 


72 


life 


4.716 


72 


56 


24 


64 


12 


4.766 


44 


56 


48 


72 


24fe 


4.667 


72 


56 


24 


64 


14 fe 


4.717 


86 


56 


24 


64 


35 


4.767 


44 


48 


56 


86 


37 


4.668 


72 


56 


24 


64 


I4fe 


4.718 


86 


56 


24 


64 


35 


4.768 


48 


64 


44 


56 


36 


4.669 


56 


44 


24 


64 


12 


4.719 


48 


64 


56 


72 


36 


4.769 


86 


48 


24 


72 


37 


4.670 


64 


48 


32 


72 


38 


4.720 


56 


44 


28 


72 


I7fe 


4.770 


86 


48 


24 


72 


37 


4.671 


44 


48 


56 


86 


38fe 


4.721 


40 


44 


48 


86 


21 'fe 


4.771 


32 


44 


56 


72 


32 'fe 


4.672 


32 


44 


48 


72 


15 fe 


4.722 


32 


40 


44 


72 


15 


4.772 


40 


64 


56 


72 


II 


4.673 


40 


64 


56 


72 


16 


4.723 


40 


48 


56 


86 


29 fe 


4.773 


32 


40 


44 


72 


12 fe 


4.674 


86 


48 


24 


72 


38fe 


4.724 


64 


40 


32 


86 


37fe 


4.774 


86 


56 


24 


64 


34 


4.675 


48 


64 


44 


56 


37 fe 


4.725 


56 


48 


44 


100 


23 


4.775 


86 


56 


24 


64 


34 


4.676 


32 


40 


44 


72 


17 


4.726 


56 


40 


28 


64 


39fe 


4.776 


56 


46 


44 


100 


2lfe 


4.677 


56 


44 


24 


64 


life 


4.727 


40 


64 


56 


72 


I3fe 


4.777 


48 


64 


56 


86 


12 


4.676 


72 


56 


24 


64 


14 


4.728 


40 


44 


56 


86 


37 


4.778 


46 


64 


56 


72 


35 


4.679 


56 


44 


28 


72 


19 


4.729 


48 


64 


56 


86 


I4fe 


4.779 


86 


56 


24 


72 


21 


4.68.0 


64 


48 


24 


56 


35 


4.730 


44 


56 


64 


86 


36 


4.780 


40 


64 


56 


72 


lOfe 


4.681 


64 


48 


24 


56 


35 


4.731 


48 


72 


64 


86 


I7fe 


4.781 


48 


72 


64 


86 


I5fe 


4.682 


40 


56 


48 


72 


lOfe 


4.732 


72 


56 


24 


64 


II 


4762 


32 


40 


44 


72 


12 


4.683 


56 


72 


64 


86 


36 


4.733 


64 


48 


32 


72 


37 


4783 


40 


44 


48 


86 


19 fe 


4.684 


40 


64 


56 


72 


I5fe 


4.734 


64 


44 


32 


86 


29 


4.784 


56 


40 


28 


72 


28fe 


4.685 


56 


44 


24 


64 


II 


4.735 


44 


48 


56 


86 


37fe 


4785 


44 


56 


48 


72 


24 


4.686 


86 


44 


24 


72 


44 


4.736 


44 


48 


56 


86 


37fe 


4.786 


64 


40 


32 


86 


36fe 


4.667 


32 


40 


48 


72 


28 fe 


4.737 


48 


64 


44 


56 


36 fe 


4787 


40 


64 


56 


72 


10 


4.688 


86 


56 


24 


64 


35 fe 


4.736 


86 


48 


24 


72 


37fe 


4786 


32 


56 


64 


72 


I9fe 


4.689 


48 


64 


56 


72 


36 fe 


4.739 


48 


64 


56 


86 


14 


4789 


40 


44 


56 


86 


36 


4.690 


32 


44 


56 


72 


34 


4.740 


72 


56 


24 


64 


lOfe 


4.790 


44 


56 


64 


86 


35 


4. 69 J 72 


48 


24 


64 


33fe 


4.741 


56 


72 


64 


86 


35 


4.791 


32 


40 


44 


72 


life 


4.692 


64 


40 


32 


86 


38 


4.742 


32 


44 


tl 


72 


!2 


4792 


64 


48 


24 


56 


33 


4.693 


56 


44 


24 


64 


lOfe 


4.743 


32 


56 


72 


21 


4793 


86 


64 


28 


72 


23fe 


4.694 


32 


44 


48 


72 


14 fe 


4.744 


32 


44 


56 


72 


33 


4.794 


64 


48 


32 


72 


36 


4.695 


40 


64 


56 


72 


15 


4.745 


56 


44 


28 


72 


16 fe 


4.795 


86 


56 


24 


72 


20 fe 


4.696 


56 


44 


28 


64 


32fe 


4.746 


86 


56 


24 


64 


34fe 


4796 


72 


48 


24 


64 


3lfe 


4.697 


40 


44 


56 


86 


37 fe 


4.747 


44 


56 


48 


72 


25 


4.797 


32 


44 


56 


72 


32 


4.698 


72 


56 


24 


64 


13 


4.748 


72 


56 


24 


64 


10 


4798 


44 


48 


56 


86 


36 fe 


4.699 


32 


„ 40 


44 


72 


16 


4.749 


48 


64 


56 


72 


35fe 


4.799 


56 


72 


64 


86 


34 



A Treatise on Milling and Milling Machines 407 





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4.800 


64 


44 


32 


86 


27 Vx 


4.850 


56 


44 


28 


72 


11/2 


4.900 


72 


44 


24 


64 


37 


4.801 


86 


48 


24 


72 


36 Vx 


4.851 


56 


40 


28 


72 


27 


4.901 


40 


44 


48 


86 


15 


4.602 


66 


56 


24 


64 


33/* 


4.652 


48 


72 


64 


86 


12 


4.902 


32 


48 


56 


72 


19 


4.803 


86 


56 


24 


64 


33/i 


4.853 


46 


72 


64 


86 


12 


4.903 


32 


48 


56 


72 


19 


4.604 


44 


56 


48 


72 


23/a 


4.854 


64 


48 


32 


72 


35 


4.904 


44 


56 


64 


86 


33 


4.605 


44 


40 


48 


66 


38/2 


4.855 


86 


56 


24 


72116/2 


4.905 


64 


44 


32 86 


25 


4.806 


44 


64 


56 


72 


26 


4.856 


48 


64 


44 


5634/2 


4.906 


56 


48 


28 


64 


16 


4.607 


48 


64 


56 


72 


34/2 


4.857 


48 


64 


44 


56 34/2 


4.907 


64 


40 


32 


86 


34/2 


4.806 


56 


48 


44 


100 


20W 


4.858 


56 


44 


26 


72 II 


4.908 


40 


44 


56 


86 


34 


4.809 


40 


44 


48 


72 


37A 


4.859 


44 


48 


56 


86 35/2 


4.909 


56 


72 


64 


86 


32 


4.810 


46 


64 


56 


86 


10 


4.860 


44 


48 


56 


86 35/2 


4.910 


86 


56 


24 


64 31/2 


4.8H 


56 


48 


28 


64 


19/1 


4.861 


48 


72 


64 


86 11/2 


4.911 


86 


56 


24 


64 


31/2 


4.812 


56 


44 


28 


72 


I3V2 


4,862 


86 


48 


24 


72 35/i 


4.912 


40 


44 


48 


86 


14/a 


4.813 


48 


72 


64 


86 


14 


4.863 


56 


40 


32 


8621 


4.913 


64 


48 


32 


72 


34 


4.614 


48 


72 


64 


86 


14 


4864 


48 


64 


56 


72 33/2 


4.914 


48 


64 


44 


56 


33/2 


4.815 


32 


40 


44 


72 


10 


4865 


40 


44 


48 


86:16/2 


4.915 


72 


48 


28 


64 


41/2 


4.816 


40 


48 


44 


72 


19 


4.866 


56 


44 


28 


72!l0'/i 


4.916 


56 


44 


28 


64 


28 


4.817 


64 


40 


32 


86 


36 


4.867 


40 


44 


64 


86 


44 


4.917 


32 


48 


56 


72 


16/2 


4.618 


44 


56 


64 


86 


34 Vx 


4.868 


56 


48 


28 


64 


17/2 


4.918 


32 


56 


64 


72 


14/2 


4.619 


40 


44 


56 


86 


35/i 


4.869 


66 


56 


24 


72 


18 


4.919 


44 


48 


56 


86 


34'/2 


4.820 


40 


44 


56 


86 


35/i 


4.870 


48 


72 


64 


86 


II 


4.920 


48 


64 


56 


72 


32/2 


4.821 


72 


48 


24 


64 


31 


4.671 


72 


48 


24 


64 


30 


4.921 


86 


56 


24 


72 


16 


4.822 


72 


48 


24 


64 


31 


4.872 


64 


48 


24 


56 


31/2 


4.922 


66 


48 


24 


72 


34/2 


4.823 


32 


44 


56 


72 


3l'/2 


4.873 


44 


56 


48 


72 


21/2 


4.923 


64 


48 


24 


56 


30/2 


4.824 


64 


48 


32 


72 


35 /a 


4.874 


32 


44 


56 


72 


30/2 


4.924 


32 


44 


56 


72 


29/2 


4.625 


64 


48 


32 


72 


35 ft 


4.875 


40 


56 


64 


86 


23/4 


4.925 


56 


40 


32 


86 


19 


4.626 


40 


44 


48 


86 


16 


4.876 


44 


56 


64 


86 


33/2 


4.926 


86 


64 


28 


72 


19/2 


4.827 


48 


64 


44 


56 


35 


4,877 


64 


40 


32 


86 


35 


4.927 


32 


40 


48 


72 


22/2 


4.828 


86 


64 


28 


72 


22 Vz 


4.878 


48 


72 


64 


8610/2 


4.928 


40 


48 


56 


72 


40/2 


4.629 


44 


48 


56 


86 


36 


4,879 


40 


44 


56 


86 1 34/2 


4.929 


32 


56 


64 


72 


14 


4.830 


86 


56 


24 


64 


33 


4.880 


86 


44 


24 


72141 /2 


4.930 


56 


48 


26 


64 


15 


4.831 


86 


48 


24 


72 


36 


4.681 


56 


72 


64 


86 32/2 


4.931 


44 


56 


64 


86 


32/2 


4.832 


86 


48 


24 


72 


36 


4.882 


86 


56 


24 


72 17/2 


4.932 


72 


44 


24 


64 


36/2 


4.833 


32 


40 


48 


72 


25 


4883 


32 


56 


64 


7Zil6 


4.933 


86 


56 


24 


72 


15/2 


4.834 


46 


72 


64 


86 


13 


4.884 


86 


56 


24 


64 32 


4.934 


40 


44 


48 


86 


13/2 


4.835 


48 


64 


40 


56 


25/2 


4.885 


48 


64 


44 


56| 34 


4.935 


56 


72 


64 


86 


31/2 


4.836 


48 


64 


56 


72 


34 


4.666 


4& 


64 


44 


56^34 


4.936 


64 


40 


32 


86 


34 


4.837 


40 


56 


64 


66 


24/2 


4.887 


56 


40 


44 


100 ! 37/2 


4.937 


56 


32 


28 


72 


43/z 


4.638 


56 


48 


44 


100 


19/2 


4.888 


32 


46 


56 


72 19/2 


4938 


44 


56 


48 


72 


19/2 


4.639 


40 


44 


48 


86 


17/2 


4.689 


44 


48 


56 


86; 35 


4.939 


32 


56 


64 


72 


13/2 


4.840 


56 


48 


28 


64 


l6'/2 


4.890 


44 


48 


56 


66 


35 


4.940 


32 


56 


64 


72 


13/2 


4.641 


56 


44 


28 


72 


12 


4.891 


32 


40 


48 


72 


23/2 


4.941 


56 


48 


28 


64 


14/2 


4.842 


64 


44 


32 


72 


4l/i 


4.892 


86 


48 


24 


72 


35 


4.942 


64 


48 


32 


72 


33/z 


4.643 


48 


72 


64 


86 


12/2 


4.893 


40 


56 


64 


86 


23 


4.943 


72 


48 


24 


64 


28/2 


4.844 


48 


72 


64 


86 


12/2 


4.894 


56 


48 


28 


64 


16/2 


4.944 


40 


44 


46 


86 


13 


4.845 


32 


56 


64 


72 


17/2 


4,695 


32 


56 


64 


72 


15/2 


4.945 


86 


56 


24 


72 


15 


4.846 


64 


48 


24 


56 


32 


4,896 


72 


48 


24 


64 


29/2 


4.946 


56 


48 


44 


100 


15/2 


4.647 


64 


40 


32 


86 


35/2 


4.897 


40 


48 


56 


66 


25/i 


4.947 


48 


64 


56 


72 


32 


4.846 


64 


40 


32 


86 


35/2 


4.896 


64 


48 


24 


56 


31 


4.948 


44 


48 


56 


86 


34 


4.849 


40 


44 


56 


86 


35 


4.899 


32 


44 


56 


72 


30 


4.949 


64 


48 


24 


56 


30 



408 



The Cincinnati Milling Machine Company 





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4.950 


32 


56 


64 72 


13 


5.Q00 


48 


64 


56 


72 


31 


5.050 48 


64 


40 


56 19/2 


4.351 


86 


48 


24 


7Z 


34 


5.001 


56 


48 


28 


64 


11/* 


5.051; 48 


64 


44 


56,31 


4.952 


40 


48 


44 


72 


13/a 


5.002 


56 


48 


44 


100 


13 


5.052; 48 


64 


56 


72J30 


4.953 


44 


56 


48 


72 


19 


5.003 


32 


56 


64 


72 


10 


5.053J 64 


48 


32 


721 31/* 


4.954 


40 


44 


48 86 


12/* 


5.004 


56 


44 


28 


64 


26 


5.054 ! 56 


40 


32 


8614 


4.955 


56 


40 


28 


64 


36 


5.005 


56 


44 


28 


64 


26 


5.055J 56 


48 


44 


lOOilO 


4.956 


86 


56 


24 


72 


14/* 


5.006 


44 


48 


56 


86 


33 


5.056 72 


48 


24 


64|26 


4.957 


40 


48 


56 


86 


24 


5.007 


86 


56 


24 


72 


12 


5.057 32 


40 


48 


72' 18/* 


4.958 


44 


56 


64 


66 


3*2 


5.008 


86 


46 


24 


72 


33 


5.058 56 


32 


28 


7242 


4.959 


44 


56 


64 


86 


32 


5.009 


86 


48 


24 


72 


33 


5.059 86 


64 


28 


7214'/* 


4.960 


32 


56 


64 


72 


12/* 


5.010 


56 


48 


28 


64 


II 


5.060! 86 


64 


28 


72 14/2 


4.961 


56 


72 


64 


86 


31 


5.011 


56 


48 


44 


100 


12/2 


5.061 86 


56 


24 


64 28'/* 


4.962 


86 


56 


24 


64 


30/* 


5.012 


44 


56 


64 


86 


31 


5.062: 44 


48 


56 


86 32 


4.963 


40 


44 


48 


86 


12 


5.018 


56 


72 


64 


86 


30 


5.063 32 


44 


56 


72 26/* 


4.964 


72 


44 


24 


64 


36 


5.014 


56 


44 


32 


64 


38 


5.064^ 86 


48 


24 


72 32 


4.965 


64 


40 


32 


86 


33/* 


5.015 


40 


48 


44 


72 


10 


5.065! 86 


48 


24 


72 32 


4.966 


72 


48 


24 


64 


28 


5.016 


40 


48 


44 


72 


10 


5.066' 40 


48 


56 


86 21 


4.967 


72 


48 


24 


64 


28 


5.017 


56 


40 


28 


64 


35 


5.067; 56 


44 


28 


64 24/* 


4.96ft 


56 


40 


32 


86 


17/* 


5.018 


32 


44 


56 


72J27/2 


5.068 64 


48 


24 


56 27/* 


4.969 


32 


56 


64 


72 


12 


5.019 


56 


48 


26 


6410/* 


5.069 64 


44 


32 


86 20/* 


4.970 


64 


48 


32 


72 


33 


5.020 


40 


44 


56 


86 


32 


5.070 ! 40 


56 


64 


86 17'/* 


4.971 


32 


44 


56 


72 


28 /* 


5.021 


64 


40 


32 


86 


32/* 


5.071 1 66 


64 


28 


72 14 


4.972 


40 


44 


46 


86 


11/* 


5.022 


64 


40 


32 


86 


32/* 


5.0721 32 


48 


56 


7212 


4.973 


48 


64 


56 


72 


31 /* 


5.023 


86 


64 


28 


72 


16 


5.073 40 


48 


56 


72 38/* 


4.974 


48 


64 


56 


72 


31 /* 


5.024 


86 


64 


28 


72 


16 


5.074 40 


44 


56 


86 31 


4.975 


44 


64 


56 


72 


ZWz 


5.025 


64 


48 


32 


72 


32 


5.075 40 


44 


56 


B6j3l 


4.976 


40 


46 


56 


86 


23 Vz 


5.026 


64 


48 


32 


72 32 


5.076 


64 


44 


24 


56 35/* 


4.977 


44 


48 


56 


86 


33/i 


5.027 


56 


48 


28 


64 


10 


5.077 


64 


40 


32 


86 31/* 


4.978 


44 


48 


56 


86 


33/z. 


5.028 


72 


48 


28 


64 


40 


5.078 48 


64 


44 


56 30'/* 


4.979 


40 


56 


64 


86 


20 Vz 


5.029 


44 


40 


48 


86 


35 


5.079 64 


48 


32 


72 31 


4.980 


86 


48 


24 


72 


33/2 


5.030 


56 


48 


44 


100 


11/2 


5.O8O1 64 


48 


32 


72 31 


4.981 


40 


44 


48 


86 


II 


5.031 


32 


48 


56 


72 


14 


5.081 32 


48 


56 


72 11/* 


4.982 


40 


48 


44 


72 


12 


5.032 


56 


40 


32 


86 


15 


5.062! 86 


64 


28 


72 13/2 


4.983 


56 


48 


28 


64 


12/2 


5.033 


86 


56 


24 


72 


10/* 


5.083 44 


56 


46 


72 14 


4984 


32 


48 


56 


72 


16 


5.034 


44 


48 


56 


86 


32/* 


5.084 1 32 


44 


56 


72 26 


4.985 


44 


56 


64 


86 


31/2 


5.035 


44 


56 


48 


72 


16 


5.085 86 


56 


24 


64 28 


4.986 


56 


40 


28 


64 


35/2 


5.036 


86 


64 


28 


72 


15/* 


5.086 56 


40 


32 


86 12'/* 


4.987 


56 


72 


64 


86 


30/2 


5.037 


66 


48 


24 


72 


32/2 


5.087 56 


72 


64 


86 28'/* 


4.988 


86 


56 


24 


64 


30 


5.038 


44 


56 


64 


86 


30/* 


5.088 44 


56 


64 


86 29/* 


4.989 


72 


48 


24 


64 


27/2 


5.039 


56 


48 


44 


100 


II 


5.089 44 


48 


56 


86 31/* 


4.990 


72 


48 


24 


64 


27/2 


5.040 


32 


44 


56 72 


27 


5.090i 32 


48 


56 


72 II 


4.991 


40 


48 


44 


72 


11/2 


5.041 


32 


44 


56 


72 


^7 


5.091 64 


48 


24 


56 27 


4.992 


56 


48 


28 


64 


12 


5.042 


32 


48 


56 


72113/2 


5.092 86 


48 


24 


72 31/* 


4.993 


64 


40 


32 


86 


33 


5.043 


56 


40 


32 


86 14/* 


5.093 44 


56 


48 


72 13/* 


4.994 


64 


40 


32 


86 


33 


5.044 


64 


44 


24 


56 


36 


5.094 56 


44 


48 


100 33'/2 


4.995 


32 


44 


56 


72 


28 


5.045 


64 


48 


24 


56 


28 


5.095. 56 


40 


32 


8612 


4.996 


32 


48 


56 


72 


15/2 


5.046 


56 


44 


28 


64 


25 


5.096; 86 


48 


28 


72 43 


4.997 


48 


64 


44 


56 


32 


5.047 


56 


48 


44 


100 10/2 


5.0971 40 


56 


64 


86 16/* 


4.998 


64 


46 


32 


72 


32/* 


5.048 


40 


44 


56 


86|3I/* 


5.096: 72 


48 


24 


64 25 


4.999 


40| 48 


44 


72 


II 


5.049 


64 


40 


32 


86|32 


5.099, 44 64 


56 


72 17/* 



A Treatise on Milling and Milling Machines 409 





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a 
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id 


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ft: 
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a 

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ft: 
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Id 

o 

Id 

ft: 


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H 


o 


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o 


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o 


id 




o 


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h 


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Id 


a 


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z 


Z 


ft: 


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O 


a: 


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a: 


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a 


a: 


Z 


Z 


tr 


_i 


< 


< 


— 


• 


< 


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< 


< 


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ni 


< 


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< 


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Id 


ft 


zl 


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01 


O 


< 


_J 


O 


V* 


CM 


O 


< 


5.100 


32 


40 


48 


72 


17 


5.150 


48 


64 


56 


72 


28 


5.200 


64 


48 


24 


56 


24 ft 


5.101 


40 


44 


56 


86 


30 '/2 


5.151 


32 


40 


48 


72 


15 


5.201 


40 


48 


64 


86 


33 


5.102 


46 


64 


56 


72 


29 


5.152 


40 


44 


56 


86 


29ft 


5.202 


56 


72 


64 


86 


26 


5.103 


46 


64 


44 


56 


30 


5.153 


40 


44 


56 


86 


29 ft 


5.203 


40 


44 


56 


86 


28ft 


5.104 


64 


40 


32 


86 


31 


5.154 


48 


64 


44 


56 


29 


5.204 


72 


44 


24 


64 


32 


5.105 


40 


44 


64 


86 


41 


5.155 


86 


40 


24 


72 


44 


5.205 


64 


32 


28 


72 


46 


5.106 


64 


48 


32 


72 


30/i 


5.156 


64 


40 


32 


86 


30 


5.206 


32 


40 


48 


72 


12ft 


5.107 


56 


40 


28 


64 


33 ft 


5.157 


56 


72 


64 


86 


27 


5.207 


64 


40 


32 


86 


29 


5.106 


66 


56 


24 


64 


27ft 


5.156 


64 


46 


32 


72 


29ft 


5.208 


64 


40 


32 


66 


29 


5.109 


46 


64 


40 


56 


17ft 


5.159 


72 


46 


24 


64 


23 ft 


5.209 


40 


56 


64 


86 


lift 


5.110 


56 


72 


64 


86 


28 


5.160 


40 


48 


56 


86 


18 


5.210 


44 


56 


64 


86 


27 


5. Ill 


56 


72 


64 


86 


28 


5.161 


64 


44 


32 


86 


17ft 


5.211 


72 


44 


24 


56 


42 


5. lie 


66 


64 


28 


72 


12 


5.162 


48 


64 


40 


56 


15ft 


5.212 


72 


44 


24 


56 


42 


5.113 


56 


40 


32 


86 


n 


5.163 


44 


56 


64 


66 


28 


5.213 


56 


44 


32 


64 


35 


5.114 


44 


56 


64 


86 


29 


5.164 


44 


64 


56 


72 


15 


5.214 


56 


32 


28 


72 


40 


5.115 


40 


48 


56 66 


l9/i 


5.165 


44 


64 


56 


72 


15 


5.215 


72 


48 


24 


64 


22 


5.116 


44 


48 


56: 86 


31 


5.166 


56 


40 


28 


64 


32ft 


5.216 


72 


48 


24 


64 


22 


5.117 


64 


44 


32! 86 


19 


5.167 


56 


40 


44 


100 


33 


5.217 


64 


56 


26 


48 


38ft 


5.116 


72 


48 


24 


64 


24ft 


5.168 


32 


44 


56 


72 


24 


5.ZI6 


40 


56 


64 


86 


II 


5.119 


66 


46 


24 


72 


31 


5.169 


44 


46 


56 


86 


30 


5.219 


86 


56 


24 


64 


25 


5.120 


44 


40 


48 


86 


33ft 


5.170 


72 


44 


24 


56 


42ft 


5.220 


48 


64 


56 


72 


26ft 


5.121 


86 


64 


28 


72 


lift 


5.171 


72 


44 


24 


56 


42ft 


5.221 


44 


48 


56 


86 


29 


5.122 


56 


40 


32 


86 


10 Vi 


5.172 


86 


48 


24 


72 


30 


5.222 


40 


44 


48 


72 


30ft 


5.123 


44 


56 


46 


72 


12 


5.173 


46 


64 


56 


72 


27 ft 


5.223 


86 


46 


24 


72 


29 


5.124 


44 


56 


48 


72 


12 


5.174 


48 


64 


56 


72 


27ft 


5.224 


56 


72 


64 


86 


25ft 


5.125 


56 


44 


28 


64 


23 


5.175 


32 


40 


48 


72 


14 


5.225 


48 


56 


64 


86 


35 


5.126 


46 


64 


56 


72 


26/i 


5.176 


86 


56 


24 


64 


26 


5.226 


32 


44 


56 


72 


22ft 


5.127 


40 


44 


56 


86 


30 


5.177 


44 


64 


56 


72 


14ft 


5.227 


40 


44 


56 


86 


28 


5.126 


64 


40 


28 


72 


34ft 


5.178 


40 


44 


56 


86 


29 


5.228 


64 


44 


32 


86 


15 


5.129 


48 


64 


44 


56 


29 ft 


5.179 


48 


64 


44 


56 


26ft 


5.229 


40 


48 


56 


86 


15ft 


5.130 


64 


40 


32 


86 


30 ft 


5.160 


56 


72 


64 


86 


26 ft 


5.230 


44 


64 


56 


72 


12 


5.131 


86 


56 


24 


64 


27 


5.181 


56 


44 


28 


64 


21ft 


5.231 


40 


46 


64 


86 32ft 


5.132 


64 


48 


32 


72 


30 


5.182 


64 


40 


32 


86 


29 ft 


5.232 


64 


40 


32 


86 


28 ft 


5. 133 


44 


56 


48 


72 


lift 


5.183 


64 


48 


32 


72 


29 


5.233 


64 


40 


32 


86 


28ft 


5.134 


56 


72 


64 


86 


27ft 


5.184 


86 


44 


24 


64 


45 


5.234 


72 


48 


24 


64 


21ft 


5.135 


40 


56 


64 


66 


15 


5.165 


56 


40 


48 


100 


39 ft 


5.235 


40 


56 


64 


86 


10 


5.136 


64 


46 


24 56 


26 


5.186 


44 


56 


64 


86 


27 ft 


5.236 


56 


44 


48 


100 


31 


5.137 


56 


40 


26 64 


33 


5.187 


44 


46 


64 


86 


40 ft 


5.237 


56 


44 


46 


100 


31 


5.136 


44 


56 


64 


86 


28% 


5.188 


32 


44 


56 


72 


23ft 


5.238 


48 


44 


56 


86 


42ft 


5.133 


72 


46 


24 


64 


24 


5.189 


64 


44 


32 


66 


16 ft 


5.239 


44 


40 


56 


86 


43 


5.140 


40 


44 


48 


72 


32 


5.190 


40 


56 


64 


66 


12 ft 


5.240 


86 


56 


24 


64 


24ft 


5.141 


40 


48 


64 


66 


34 


5.191 


40 


46 


64 


72 


45ft 


5.241 


86 


56 


24 


64 


24ft 


5.142 


44 


56 


48 


72 


11 


5.192 


56 


40 


28 


72 


17ft 


5.242 


72 


48 


28 


64 


37 


5.143 


44 


46 


56 


86 


30 ft 


5.193 


48 


56 


64 


86 


35 ft 


5.243 


48 


64 


56 


72 


26 


5.144 


40 


44 


64 


86 


40 ft 


5.194 


56 


40 


28 


64 


32 


5.244 


32 


40 


48 


72 


10ft 


5.145 


40 


46 


56 


86 


IS'/z 


5.195 


44 


48 


56 


86 


29 ft 


5.245 


32 


44 


56 


72 


22 


5.146 


86 


48 


24 


72 


30 ft 


5.196 


32 


40 


48 


72 


13 


5.246 


44 


48 


56 


86 


28ft 


5.147 


86 


64 


26 


72 


10 


5.197 


48 


64 


56 


72 


27 


5.247 


64 


40 


28 


72 


32 ft 


5.146 


32 


44 


56 


72 


24ft 


5.198 


86 


46 


24 


72 


29ft 


5.248 


66 


46 


24 


72 


28ft 


5.149 


46 


64 


40 


56 


16 


5.199 


64 


46 


24 


56 


24 ft 


5.249 


44 


64 


56 


72 


II 



410 



The Cincinnati Milling Machine Company 





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ti 


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5.250 


56 


40 


28 


64 


31 


5.300 


40 


44 


48 


72 


29 


5.350 


72 


48 


24 


64 


18 


5.251 


40 


44 


56 


86 


27ft 


5.301 


86 


56 


24 


64 


23 


5.351 


64 


40 


32 


86 


26 


5.252 


32 


40 


48 


72 


10 


5.302 


72 


48 


24 


64 


l9/i 


5.352 


64 


40 


32 


86 


26 ! 


5.253 


40 


48 


56 


86 


14ft 


5.303 


64 


48 


32 


72 


26/i 


5.353 


56 


40 


28 


72 


IO/i 


5.254 


64 


56 


28 


48 


38 


5.304 


56 


40 


26 


72 


13 


5.354 


40 


56 


64 


72 


32/i 


5.255 


44 


56 


64 


86 


26 


5.305 


64 


40 


32 


86 


27 


5.355 


40 


56 


64 


72 


32/i 


5.256 


64 


48 


32 


72 


27/* 


5.306 


64 


40 


28 


72 


31 ft 


5.356 


72 


40 


24 


64 


37 '/i 


5.257 


64 


40 


32 


86 


28 


5.307 


40 


48 


56 


86 


12 


5.357 


56 


40 


28 


64 


29 


5.25& 


44 


64 


56 


72 


10 ft 


5.308 


48 


64 


56 


72 


24 ft 


5.358 


86 


56 


24 


64 


21ft, 


5.259 


48 


64 


40 


56 


It 


5.309 


40 


48 


56 


72 


35 


5.359 


64 


56 


28 


48 


36 ft 


5.260 


64 


46 


24 


56 


23 


5.310 


56 


44 


28 


64 


(7'/i 


5.360 


64 


44 


32 


72 


34 


5.261 


86 


56 


24 


64 


24 


5.311 


44 


56 


64 


72 


40/i 


5.361 


56 


40 


28 


72 


10 


5.262 


64 


44 


52 


86 


13ft 


5.312 


64 


44 


32 


86 


II 


5.362 


46 


64 


44 


56 


24'/i 


5.26* 


32 


44 


56 


72 


21ft 


5.313 


64 


44 


32 


86 


II 


5.363 


44 


40 


48 


72 


43 


5.264 


32 


44 


56 


72 


21ft 


5.314 


72 


44 


24 


64 


30 


5.364 


72 


48 


24 


64 


17/2 


5.265 


48 


64 


56 


72 


25ft 


5.315 


56 


40 


28 


72 


l2'/i 


5.365 


44 


48 


56 


86 


26 


5.266 


44 


64 


56 


72 


10 


5.316 


64 


46 


24 


56 


2l'/i 


5.366 


56 


44 


26 


64 


15ft 


5.267 


56 


72 


64 


86 


24/4 


5.317 


40 


48 


56 


86 


lift 


5.367 


56 


72 


64 


86 


22 


5.266 


72 


48 


24 


64 


20 ft 


5.318 


44 


48 


56 


86 


27 


5.368 


86 


48 


24 


72 


26 


5.269 


72 


48 


24 


64 


20 ft 


5.319 


48 


64 


44 


56 


25ft 


5.369 


48 


64 


56 


72 


23 


5.270 


44 


48 


56 


86 


28 


5.320 


44 


56 


64 


86 


24/i 


5.370 


64 


46 


24 


56 


20 


5.271 


56 


40 


28 


72 


14ft 


5.321 


66 


48 


24 


72 


27 


5.371 


64 


48 


32 


72 


25 


5.272 


86 


44 


24 


64 


44 


5.322 


64 


44 


32 


86 


10 ft 


5.372 


72 


44 


24 


56 


40 


5.273 


86 


48 


24 


72 


28 


5.323 


44 


40 


56 


86 


42 


5.373 


40 


48 


64 


72 


43ft 


5.274 


48 


64 


44 


56 


26ft 


5.324 


86 


64 


40 


72 


44ft 


5.374 


64 


40 


32 


86 


25ft 


5.275 


40 


44 


56 


86 


27 


5.325 


56 


40 


28 


72 


12 


5.375 


86 


44 


26 


72 


45 


5.276 


46 


64 


40 


56 


10 


5.326 


64 


46 


32 


72 


26 


5.376 


56 


64 


40 


48 


42ft 


5.277 


44 


56 


64 


86 


25ft 


5.327 


40 


44 


48 


72 


28'/z 


5.377 


86 


56 


24 


64 


21 


5.278 


56 


40 


28 


64 


30 ft 


5.328 


64 


40 


32 


86 


26'/i 


5.378 


66 


56 


32 


72 


36 


5.279 


64 


48 


24 


56 


22 /i 


5.329 


64 


40 


32 


86 


26/i 


5.379 


72 


48 


24 


64 


17 


5.280 


64 


48 


32 


72 


27 


5.330 


64 


44 


32 


86 


10 


5.380 


32 


44 


56 


72 


16 


5.281 


64 


40 


32 


86 


27/2 


5.331 


56 


40 


28 


64 


29/i 


5.381 


44 


48 


56 


72 


41 


5.282 


56 


40 


28 


72 


14 


5.332 


56 


40 


48 


100 


37/2 


5.382 


44 


56 


64 


86 


23 


5.283 


72 


40 


24 


64 


38ft 


5.333 


32 


44 


56 


72 


19/1 


5.383 


48 


64 


44 


56 


24 


5.284 


64 


44 


32 


86 


12ft 


5.334 


64 


46 


24 


56 


21 


5.384 


48 


64 


44 


56 


24 


5.285 


64 


40 


32 


72 


42 


5.335 


64 


46 


24 


56 


21 


5.385 


56 


72 


64 


86 


21/2 


5.286 


48 


64 


56 


72 


25 


5.336 


40 


44 


56 


72 


41 


5.386 


64 


48 


24 


56 


19/1 


5.287 


48 


64 


56 


72 


25 


5.337 


40 


44 


56 


72 


41 


5.387 


44 


48 


56 


86 


25ft 


5.288 


56 


72 


64 


86 


24 


5.338 


86 


48 


26 


72 


40 


5.388 


44 


48 


56 


86 


25ft 


5.289 


48 


56 


64 


86 


34 


5.339 


56 


44 


28 


64 


16ft 


5.389 


48 


64 


56 


72 


22ft 


5.290 


56 


44 


48 


100 


30 


5.340 


86 


56 


24 


64 


22 


5.390 


86 


48 


24 


72 


25ft 


5.291 


56 


44 


48 


100 


30 


5.341 


48 


64 


44 


56 


25 


5.391 


56 


44 


28 


64 


t4/i 


5.292 


72 


44 


24 


56 


41 


5.342 


44 


48 


56 


86 


26/2 


5.392 


64 


48 


32 


72 


24/2 


5.293 


72 


44 


24 


56 


41 


5.343 


40 


44 


56 


66 


25/2 


5.393 


72 


48 


24 


64 


16 ft 


5.294 


44 


48 


56 


86 


27ft 


5.344 


86 


46 


24 


72 


26/i 


5.394 


86 


56 


24 


64 


20 ft 


5.295 


44 


48 


56 


86 


27/i 


5.345 


86 


48 


24 


72 


26/2 


5.395 


32 


44 


56 


72 


17ft 


5.296 


56 


44 


28 


64 


16 


5.346 


86 


48 


28 


64 


47 


5.396 


64 


40 


32 


66 


25 


5.297 


86 


48 


24 


72 


27 'A 


5.347 


56 


72 


64 


86 


22 ft 


5.397 


56 


44 


32 


64 


32 


5.298 


40 


44 


56 


86 


26/i 


5.348 


56 


72 


64 


66 


22/i 


5.398 


40 


48 


64 


86 


29ft 


5.299 


44 


56 


64 


86 


25 


5.349 


32 


44 


56 


72 


19 


5.399 


64 


44 


24 


56 


30 



A Treatise on Milling and Milling Machines 411 





or 
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IV 


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_J 


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O 


111 


Id 


SI 


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Z 


Id 


Id 


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CM 


& 


< 


_J 


O 


T* 


CM 


O 


< 


5.400 


56 


32 


28 


72 


37 ft 


5.450 


64 


48 


24 


56 


17ft 


5.500 


64 


32 


28 


72 


45 


5.401 


56 


40 


32 


64 


39 ft 


5.451 


32 


44 


56 


72 


15ft 


5.501 


64 


40 


32 


86 


22ft 


5.402 


44 


56 


64 


86 


22/i 


5.452 


72 


56 


32 


64 


32 


5.502 


48 


64 


44 


56 


21 


5.403 


56 


72 


64 


86 


21 


5.453 


44 


48 


56 


86 


24 


5.503 


56 


64 


40 


48 


41 


5.404 


46 


64 


44 


56 


23ft 


5.454 


72 


40 


24 


56 


45 


5.504 


86 


64 


40 


72 


42 ft 


5.405 


64 


44 


28 


56 


42 


5.455 


64 


48 


32 


72 


23 


5.505 


56 


72 


64 


86 


16 


5.406 


44 


40 


56 


86 


41 


5.456 


86 


48 


24 


72 


24 


5.506 


64 


46 


24 


56 


15 ft 


5.407 


64 


40 


32 


72 


40 ft 


5.457 


56 


40 


28 


64 


27 


5.507 


86 


56 


24 


64 


17 


5.406 


40 


44 


56 


66 


24 


5.458 


72 


46 


24 


64 


14 


5.508 


40 


44 


56 


86 


21ft 


5.409 


66 


40 


24 


72 


41 


5.459 


44 


56 


64 


86 


21 


5.509 


40 


44 


56 


86 


21ft 


5.410 


44 


48 


56 


86 


25 


5.460 


64 


40 


32 


86 


23ft 


5.510 


72 


56 


32 


64 


31 


5.41 1 


72 


44 


24 


56 


39 ft 


5.461 


86 


56 


24 


64 


18ft 


5.511 


56 


44 


32 


64 


30 


5.412 


66 


48 


24 


72 


25 


5.462 


86 


56 


24 


64 


18 ft 


5.512 


44 


56 


64 


86 


19ft 


5.413 


66 


48 


24 


72 


25 


5.463 


48 


64 


56 


72 


20 ft 


5.513 


56 


40 


44 


100 


26 Vz 


5.414 


64 


48 


32 


72 


24 


5.464 


48 


64 


44 


56 


22 


5.514 


64 


48 


32 


72 


21 ft 


5.415 


66 


64 


40 


72 


43/a 


5.465 


44 


56 


64 


72 


38/i 


5.515 


44 


48 


56 


86 


22 ft 


5.416 


40 


44 


56 


72 


40 


5.466 


56 


44 


28 


64 


II 


5.516 


56 


40 


32 


64 


38 


5.417 


40 


46 


64 


72 


43 


5.467 


56 


44 


48 


100 


26 ft 


5.517 


86 


48 


24 


72 


22ft 


5.416 


64 


40 


32 


86 


24/i 


5.466 


64 


40 


28 


72 


28ft 


5.518 


86 


48 


24 


72 


22 ft 


5.419 


64 


48 


24 


56 


18ft 


5.469 


40 


44 


56 


86 


22ft 


5.519 


64 


48 


24 


56 


15 


5.420 


72 


46 


24 


64 


15ft 


5.470 


72 


48 


24 


64 


13 ft 


5.520 


64 


40 


32 


86 


22 


5.421 


44 


56 


64 


86 


22 


5.471 


56 


32 


28 


72 


36ft 


5.521 


64 


40 


32 


86 


22 


5.422 


56 


72 


64 


86 


20 ft 


5.472 


56 


72 


64 


86 


19 


5.522 


86 


56 


24 


64 


16ft 


5.423 


72 


56 


32 


64 


32 ft 


5.473 


56 


72 


64 


86 


19 


5.523 


32 


44 


56 


72 


12ft 


5.424 


32 


44 


56 


72 


16 'ft 


5.474 


44 


48 


56 


86 


23'ft 


5.524 


72 


44 


28 


64 


39 ft 


5.425 


46 


64 


44 


56 


23 


5.475 


64 


48 


32 


72 


22 Vz 


5.525 


86 


44 


24 


72 


32 


5.426 


64 


44 


24 


56 


29 ft 


5.476 


40 


48 


64 


66 


28 


5.526 


64 


40 


32 


72 


39 


5.427 


46 


64 


56 


72 


21ft 


5.477 


86 


46 


24 


72 


23 ft 


5.527 


40 


44 


56 


86 


21 


5.426 


44 


56 


64 


72 


39 


5.478 


56 


40 


32 


64 


38ft 


5.528 


44 


56 


64 


86 


19 


5.429 


40 


44 


56 


86 


23 ft 


5.479 


64 


48 


24 


56 


16ft 


5.529 


72 


48 


32 


64 


42ft 


5.430 


86 


64 


32 


56 


45 


5.480 


48 


56 


64 


72 


44 


5.530 


72 


48 


32 


64 


42ft 


5.431 


44 


48 


56 


86 


24ft. 


5.481 


64 


40 


32 


86 


23 


5.531 


72 


48 


24 


64 


10 ft 


5.432 


44 


48 


56 


86 


24ft 


5.482 


48 


44 


56 


86 


39ft 


5.532 


64 


48 


32 


72 


21 


5.433 


72 


48 


24 


64 


15 


5.483 


46 


64 


44 


56 


21ft 


5.533 


32 


44 


56 


72 


12 


5.434 


86 


48 


24 


72 


24ft 


5.484 


72 


44 


28 


64 


40 


5.534 


44 


48 


56 


86 


22 


5.435 


64 


46 


32 


72 


23 ft 


5.485 


72 


46 


32 


64 


43 


5.535 


56 


72 


64 


86 


17 


5.436 


56 


44 


28 


64 


12ft 


5.486 


86 


56 


32 


72 


36ft 


5.536 


86 


56 


24 


64 


16 


5.437 


56 


40 


48 


100 


36 


5.487 


44 


40 


56 


86 


40 


5.537 


86 


48 


24 


72 


22 


5.436 


32 


44 


56 


72 


16 


5.488 


72 


44 


24 


56 


38ft 


5.538 


48 


64 


44 


56 


20 


5.439 


64 


40 


32 


86 


24 


5.489 


40 


44 


56 


86 


22 


5.539 


72 


48 


24 


64 


10 


5.440 


44 


56 


64 


86 


21ft 


5.490 


86 


44 


24 


64 


41ft 


5.540 


64 


40 


32 


86 


21 ft 


5.441 


72 


48 


28 


64 


34 


5.491 


86 


48 


28 


72 


38 


5.541 


44 


46 


56 


72 


39 


5.442 


46 


44 


56 


86 


40 


5.492 


66 


56 


24 


64 


I7'ft 


5.542 


44 


40 


48 


86 


25ft 


5.443 


56 


44 


48 


100 


27 


5.493 


86 


56 


24 


64 


17 ft 


5.543 


32 


44 


56 


72 


lift 


5.444 


46 


64 


44 


56 


22 ft 


5.494 


44 


48 


56 


86 


23 


5.544 


64 


46 


24 


56 


14 


5.445 


46 


64 


44 


56 


22 '/z 


5.495 


44 


48 


56 


86 


23 


5.545 


40 


44 


56 


86 


20ft 


5.446 


46 


64 


56 


72 


21 


5.496 


46 


56 


64 


86 


30ft 


5.546 


40 


44 


56 


86 


20 'ft 


5.447 


86 


44 


24 


64 


42 


5.497 


86 


46 


24 


72 


23 


5.547 


46 


64 


56 


72 


18 


5.446 


44 


48 


64 


86 


37 


5.498 


46 


64 


56 


72 


19 ft 


5.548 


48 


64 


56 


72 


18 


5.449 


40 


44 


56 


86 


23 


5.499 


48 


64 


56 


72 


19 ft 


5.549 


72 


40 


24 


56 


44 



412 



The Cincinnati Milling Machine Company 





o 


bi 

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bJ 

u 


o 

bi 

X 
a: 


2 

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ft: 
o 
tn 






£ 

ft: 
o 


bi 

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bJ 

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Z 
ft: 


i 

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o 

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z 


us 


Z 






z 


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z 






o 


H 


—7 


o 


U 


. 


o 


h- 




o 


bJ 




o 


UJ 


1- 


o 


bi 


a 


ft: 


Z 


z 


(T 


_J 


a 


ft: 


Z 


z. 


Cc 


_i 


o 


QC 


Z 


z 


a: 


_i 


< 


< 


~ 


at 


< 


CD 


< 


< 


"^ 


ot 


< 


© 


< 


< 




. 


< 


© 


u 


bi 


fcl 


z\ 


a 


z 


bJ 


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3 


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Z 


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bi 


53 


II 


bi 


Z 


_i 


© 


t* 


CM 


< 


j 


© 


i-i 


CM 


© 


< 


_l 


O 


*-i 


ai 


O 


< 


5.550 


56 


72 


64 


86 


16 Vz 


5.600 


86 


56 


24 


64 


I3'/1 


5.650 


48 


64 


44 


56 


16/2 


5.551 


64 


48 


32 


72 


20 /i 


5.601 


72 


44 


24 


56 


37 


5.651 


56 


72 


64 


86 


12/2 


5.552 


48 


56 


64 


86 


29 /i 


5.602 


56 


44 


48 


100 


23/i 


5.652 


64 


48 


32 


72 


17/2 


5.553 


32 


44 


56 


72 


II 


5.603 


64 


48 


32 


72 


19 


5.653 


86 


56 


24 


64 


II 


5.554 


44 


48 


56 


86 


21 fe 


5.604 


56 


72 


64 


86 


14/1 


5.654 


64 


44 


32 


72 


29 


5.555 


48 


64 


44 


56 


19 /i 


5.605 


48 


64 


44 


56 


18 


5.655 


64 


44 


32 


72 


29 


5.556 


86 


48 


24 


72 


2l/i 


5.606 


44 


56 


64 


86 


I6/1 


5.656 


86 


44 


24 


64 


39/i 


5.557 


86 


48 


24 


72 


21 Vi 


5.607 


48 


64 


56 


72 


16 


5.657 


44 


48 


56 


72 


37/2 


5.558 


64 


40 


32 


86 


21 


5.608 


40 


44 


64 


86 


34 


5.658 


44 


40 


48 


72 


39/2 


5.559 


64 


40 


32 


86 


21 


5.609 


44 


48 


56 


86 


20 


5.659 


56 


40 


28 


64 


22/2 


5.560 


48 


44 


56 


86 


38/i 


5.610 


40 


44 


56 


72 


37/i 


5.660 


48 


64 


56 


72 


14 


5.561 


44 


56 


64 


86 


18 


5.611 


86 


56 


24 


64 


13 


5.661 


44 


48 


56 


86 


18/2 


5.562 


32 


44 


56 


72 


10/* 


5.612 


86 


48 


24 


72 


20 


5.662 


56 


72 


64 


86 


12 


5.563 


40 


44 


56 


86 


20 


5.613 


64 


40 


32 


86 


l9'/i 


5.663 


86 


48 


24 


72 


18/2 


5.564 


56 


72 


64 


86 


16 


5.614 


40 


44 


56 


86 


18/2 


5.664 


86 


48 


24 


72 


16/2 


5.565 


64 


40 


32 


72 


38V* 


5.615 


86 


44 


24 


64 


40 


5.665 


48 


64 


44 


56 


16 


5.566 


56 


44 


32 


64 


29 


5.616 


56 


72 


64 


86 


14 


5.666 


40 


48 


64 


86 


24 


5.567 


64 


48 


24 


56 


13 


5.617 


72 


48 


32 


64 


4l/i 


5.667 


56 


64 


40 


48 


39 


5.568 


64 


48 


24 


56 


13 


5.616 


64 


48 


24 


56 


10 Vz 


5.666 


40 


48 


56 


72 


29 ; 


5.569 


64 


48 


32 


72 


20 


5.619 


44 


48 


56 


72 


38 


5.669 


72 


44 


24 


64 


22/2 


5.570 


86 


40 


24 


72 


39 


5.620 


64 


48 


32 


72 


18/1 


5.670 


56 


40 


44 


100 


23 


5.571 


32 


44 


56 


72 


to 


5.621 


48 


64 


56 


72 


15/1 


5.671 


86 


56 


24 


64 


10 


5.572 


44 


48 


56 


86 


21 


5.622 


86 


56 


24 


64 


I2/i 


5.672 


48 


64 


56 


72 


13/2 


5.573 


44 


48 


56 


86 


21 


5.623 


86 


56 


24 


64 


l2*/i 


5.673 


44 


56 


64 


86 


14 


5.574 


72 


48 


32 


64 


42 


5.624 


86 


56 


32 


72 


34*/i 


5.674 


40 


48 


64 


72 


40 


5.575 


86 


48 


24 


72 


21 


5.625 


86 


56 


32 


72 


34ft 


5.675 


56 


32 


28 


72 


33/2 


5.576 


44 


56 


64 


86 


17ft. 


5.626 


72 


48 


28 


64 


31 


5.676 


40 


44 


56 


86 


16/2 


5.577 


64 


40 


32 


86 


20/i 


5.627 


44 


46 


56 


86 


19/2 


5.677 


44 


48 


56 


86 


18 


5.578 


48 


64 


56 


72 


17 


5.628 


56 


72 


64 


86 


13/2 


5.676 


64 


40 


32 


86 


17/2 


5.579 


64 


48 


24 


56 


l2'/i 


5.629 


86 


48 


24 


72 


19/2 


5.679 


48 


64 


44 


56 


15/1 


5.580 


40 


44 


56 


86 


19'/* 


5.630 


86 


48 


24 


72 


19/1 


5.680 


86 


48 


24 


72 


18 


5.58! 


40 


44 


56 


86 


19 'A 


5.631 


44 


40 


48 


86 


23/i 


5.681 


64 


44 


32 


72 


28/i 


5.582 


86 


48 


32 


72 


45/i 


5.632 


40 


46 


64 


72 


40/i 


5.682 


64 


48 


32 


72 


l6/i 


5.583 


72 


44 


24 


64 


24/i 


5.633 


86 


56 


24 


64 


12 


5.683 


48 


64 


56 


72 


13 


5.564 


72 


44 


24 


64 


24 y* 


5.634 


44 


56 


64 


86 


15/2 


5.684 


48 


64 


56 


72 


13 


5.585 


86 


44 


24 


72 


31 


5.635 


46 


64 


44 


56 


17 


5.685 


44 


56 


64 


86 


l3/i 


5.586 


64 


48 


32 


72 


19 /i 


5.636 


64 


48 


32 


72 


16 


5.686 


86 


40 


24 


72 


37/i 


5.587 


44 


40 


48 


86 


24/2 


5.637 


72 


44 


24 


56 


36/2 


5.687 


72 


40 


24 


56 


42Vi 


5.588 


86 


56 


24 


64 


14 


5.638 


56 


40 


28 


64 


23 


5.688 


40 


48 


64 


66 


23/i 


5.589 


48 


64 


44 


56 


18/1 


5.639 


40 


44 


46 


72 


21/2 


5.689 


44 


48 


64 


86 


33/i 


5.590 


40 


48 


64 


72 


41 


5.640 


56 


72 


64 


86 


13 


5.690 


48 


44 


64 


86 


45/i 


5.591 


44 


48 


56 


86 


20/2 


5.641 


72 


44 


28 


64 


38 


5.691 


40 


44 


56 


86 


16 


5.592 


44 


56 


64 


86 


17 


5.642 


64 


40 


32 


72 


37/i 


5.692 


48 


64 


44 


56 


15 


5.593 


48 


64 


56 


72 


I6/1 


5.643 


86 


56 


24 


64 


life 


5.693 


44 


48 


56 


86 


l7/i 


5.5^4 


86 


48 


24 


72 


20/i 


5.644 


44 


48 


56 


86 


19 


5.694 


64 


40 


32 


86 


17 


5.595 


56 


40 


28 


64 


24 


5.645 


44 


40 


56 


86 


38 


5.695 


46 


64 


56 


72 


12/2 


5.596 


56 


40 


28 


64 


24 


5.646 


64 


40 


32 


86 


18/2 


5.696 


86 


48 


24 


72 


17/2 


5.597 


40 


44 


56 


86 


19 


5.647 


86 


48 


24 


72 


19 


5.697 


44 


56 


64 


86 


13 


5.598 


48 


44 


56 


86 


38 


5.648 


44 


56 


64 


66 


15 


5.696 


86 


44 


24 


72 


29 


5.599 


64 


48 


24 


56 


11*1 


5.649 


56 


40 


44 


too 


23/2 


5.699 


44 


40 


48 


72 


39 



A Treatise on Milling and Milling Machines 413 





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< 


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< 


< 


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'<-! 


CM 


< 


J 


O 


i-t 


CM 


o 


< 


5.700 


56 


72 


64 


86 


10 


5.750 


64 


48 


32 


72 


14 


5.600 


64 


44 


24 


56 


21ft 


5.701 


86 


40 


24 


64 


45 


5.751 


64 


40 


32 


86 


15 


5.801 


64 


40 


32 


86 


13 


5.702 


72 


56 


32 


64 


27 ft 


5.752 


44 


48 


56 


86 


15ft 


5.802 


72 


44 


24 


64 


19 


5.703 


72 


48 


32 


64 


40/2 


5.753 


48 


64 


44 


56 


127* 


5.803 


48 


64 


44 


56 


10 


5.704 


40 


44 


56 


86 


15ft 


5.754 


44 


48 


64 


86 


32 'ft 


5.604 


44 


48 


56 


86 


I3'ft 


5.705 


40 


44 


56 


86 


15ft 


5.755 


86 


48 


24 


72 


15ft 


5.805 


44 


48 


56 


72 


35 ft 


5.706 


46 


64 


56 


72 


12 


5.756 


40 


44 


56 


86 


13 ft 


5.806 


44 


40 


48 


86 


19 


5.707 


56 


64 


40 


48 


38V* 


5.757 


40 


44 


56 


72 


35 ft 


5.807 


86 


48 


24 


72 


13ft 


5.706 


44 


48 


56 


86 


17 


5.758 


44 


56 


64 


86 


10 


5.808 


64 


44 


28 


56 


37 


5.709 


64 


40 


32 


86 


\6ft 


5.759 


56 


44 


48 


100 


19ft 


5.809 


64 


44 


28 


56 


37 


5.710 


64 


48 


32 


72 


15ft 


5.760 


86 


64 


40 


72 


39ft 


5.810 


86 


48 


28 


72 


33ft 


5.711 


86 


48 


24 


72 


17 


5.761 


86 


40 


24 


72 


36 'ft 


5. 611 


40 


44 


56 


86 


II 


5.712 


56 


40 


44 


100 


22 


5.762 


64 


48 


32 


72 


I3'ft 


5.812 


44 


48 


64 


72 


44ft 


5.713 


40 


44 


46 


72 


19'/* 


5.763 


40 


44 


64 


72 


44 ft 


5.813 


64 


40 


32 


86 


12ft 


5.714 


40 


44 


64 


72 


45 


5.764 


64 


40 


32 


86 


14ft 


5.814 


72 


44 


24 


56 


34 


5.715 


40 


46 


64 


72 


39ft 


5.765 


44 


48 


56 


86 


15 


5.815 


66 


44 


24 


64 


37ft 


5.716 


48 


64 


56 


72 


lift 


5.766 


44 


48 


56 


86 


15 


5.816 


44 


48 


56 


86 


13 


5.717 


72 


44 


28 


64 


37 


5.767 


72 


4a 


26 


64 


28 ft 


5.817 


64 


48 


32 


72 


11 


5.716 


40 


44 


56 


86 


15 


5.766 


86 


46 


24 


72 


15 


5.818 


44 


40 


48 


72 


37ft 


5.719 


44 


56 


64 


86 


12 


5.769 


56 


40 


32 


64 


34ft 


5.619 


86 


46 


24 


72 


13 


5.720 


40 


44 


56 


72 


36 


5.770 


64 


44 


26 


56 


37 ft 


5.620 


64 


44 


24 


56 


21 


5.721 


44 


40 


56 


86 


37 


5.771 


40 


46 


64 


86 


21 ft 


5.621 


40 


44 


56 


86 


10ft 


5.722 


56 


44 


48 


100 


20ft 


5.772 


56 


32 


28 


72 


32 


5.622 


72 


48 


28 


64 


27ft 


5.723 


44 


48 


56 


66 


16 ft 


5.773 


64 


56 


26 


48 


30 


5.823 


44 


40 


48 


86 


18 ft 


5.724 


64 


46 


32 


72 


15 


5.774 


64 


46 


32 


72 


(3 


5.824 


64 


40 


32 


66 


12 


5.725 


86 


44 


24 


72 


28ft 


5.775 


48 


64 


44 


56 


lift 


5.825 


64 


40 


32 


72 


35 


5.726 


86 


48 


24 


72 


16ft 


5.776 


86 


44 


24 


64 


32> 


5.826 


40 


44 


48 


72 


16 


5.727 


64 


40 


28 


72 


2* 


5.777 


64 


40 


32 


86 


14 


5.827 


44 


48 


56 


86 


12 ft 


5.728 


72 


44 


24 


64 


21 


5.778 


86 


44 


24 


64 


38 


5.826 


72 


48 


32 


64 


39 


5.729 


72 


44 


24 


64 


21 


5.779 


44 


48 


56 


86 


14ft 


5.829 


72 


48 


32 


64 


39 


5.730 


48 


64 


44 


56 


13ft 


5.780 


40 


44 


56 


86 


12ft 


5.830 


86 


46 


24 


72 


12ft 


5.731 


40 


44 


56 


86 


14 ft 


5.781 


46 


56 


64 


86 


25 


5.631 


66 


48 


24 


72 


12ft 


5.732 


44 


48 


56 


72 


36 ft 


5.782 


86 


48 


24 


72 


14ft 


5.632 


44 


40 


56 


86 


35ft 


5.733 


48 


56 


64 


86 


26 


5.783 


48 


44 


56 


66 


35ft 


5.833 


46 


64 


44 


40 


45 


5.734 


56 


40 


32 


64 


35 


5.784 


48 


44 


56 


86 


35 ft 


5.834 


64 


40 


32 


66 


lift 


5.735 


46 


64 


56 


72 


10 ft 


5.785 


64 


48 


32 


72 


12ft 


5.835 


64 


40 


32 


86 


Uft 


5.736 


86 


44 


24 


64 


38ft 


5.766 


64 


48 


32 


72 


12 'ft 


5-836 


64 


48 


32 


72 


10 


5.737 


64 


40 


32 


86 


15ft 


5.787 


72 


48 


32 


64 


39 'ft 


5.637 


40 


48 


64 


72 


38 


5.738 


44 


48 


56 


86 


16 


5.788 


86 


56 


32 


72 


32 


5.838 


44 


48 


56 


86 


12 


5.739 


44 


40 


48 


72 


38ft 


5.789 


64 


40 


32 


86 


13ft 


5.689 


44 


48 


56 


86 


12 


5.740 


44 


56 


64 


66 


II 


5.790 


64 


40 


32 


86 


13ft 


5.840 


44 


46 


56 


72 


35 


5.741 


86 


46 


24 


72 


16 


5.791 


40 


44 


56 


86 


12 


5.841 


86 


48 


24 


72 


12 


5.742 


48 


64 


44 


56 


13 


5.792 


44 


48 


56 


86 


14 


5.842 


86 


46 


24 


72 


12 


5.743 


86 


46 


28 


72 


34ft 


5.793 


56 


44 


48 


100 


18ft 


5.843 


86 


48 


28 


72 


33 


5.744 


40 


44 


56 


86 


14 


5.794 


46 


64 


44 


56 


10 'ft 


5.844 


86 


48 


28 


72 


33 


5.745 


72 


48 


32 


64 


40 


5.795 


86 


48 


24 


72 


14 


5.845 


64 


40 


32 


86 


11 


5.746 


56 


64 


40 


48 


38 


5.796 


64 


48 


32 


72 


12 


5.846 


64 


44 


28 


56 


36 ft 


5.747 


46 


44 


56 


86 


36 


5.797 


40 


48 


64 


72 


36ft 


5.847 


64 


44 


26 


56 


36 ft 


5.746 


40 


44 


46 


72 


16ft 


5.798 


86 


40 


24 


72 


36 


5.848 


72 


44 


24 


56 


33 ft 


5.749 


44 


56 


64 


86 


10 ft 


5.799 


40 


44 


64 


86 


31 


5.849 


44 


48 


56 


86 


lift 



414 



The Cincinnati Milling Machine Company 





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< 


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5.850 


86 


56 


32 


72 


31 


5.900 


56 


64 


40 


48 36 


5.950 


72 


48 


32 


64 


37ft 


5.651 


64 


40 


28 


56 


43 


5.901 


56 


44 


48 


100 15 


5.951 


64 


44 


32 


72 


23 


5.852 


66 


48 


24 


72 


life 


5.902 


56 


40 


28 


64jl5ft 


5.952 


56 


44 


48 


100 


13 


5.853 


48 


40 


56 


86 


41 ft 


5.903 


44 


40 


56 


66 34X2 


5.953 


56 


32 


28 


72 


29 


5.854| 64 


40 


32 86 


10ft 


5.904 


56 


40 


32 


64 32 ft 


5.954 


40 


48 


64 


72 


36ft 


5.855 


48 


44 


56; 86 


34ft 


5.905 


40 


44 


46 


72 13 


5.955 


44 


56 


64 


72 


31 ft 


5.856 


44 


40 


48 


72 


37 


5.906 


86 


40 


24 


72 34ft 


5.956 


56 


40 


28 


64 


13ft 


5.857 


44 


56 


64 


72 


33 


5.907 


66 


40 


24 


72 34ft 


5.957 


64 


44 


28 


56 


35 


5.858 


56 


44 


48 


100 


16/1 


5.906 


44 


48 


64 


86j30 


5.958 


64 


44 


28 


56 


35 


5.859 


44 


48 


56 


86 


II 


5.909 


86 


48 


28 


72 32 


5.959 


40 


44 


48 


72 


10ft 


5.660 


64 


40 


32 


72 


34 ft 


5.910 


72 


48 


32 


64 38 


5.960 


40 


44 


48 


72 


10ft 


5.861 


44 


48 


64 


72 


44 


5.911 


44 


48 


56 


72 34 


5.961 


56 


44 


32 


64 


20ft 


5.862 


66 


48 


24 


72 


n 


5.912 


64 


44 


24 


56 ! l8ft 


5.962 


86 


64 


40 


72 


37 


5.865 


64 


40 


32 


86 


10 


5.913 


72 


44 


24 


64il5ft 


5.963 


46 


56 


64 


72 


36ft 


5.864 


64 


40 


32 


86 10 


5.914 


56 


44 


48 


10014ft 


5.964 


64 


40 


32 


72 


33 


5.865 


64 


40 


28 


72 


19ft 


5.915 


40 


48 


64 


72 37 


5.965 


40 


48 


56 


72 


23 


5.866 


40 


56 


64 


72 


22 ft 


5.916 


40 


48 


64 


72j 37 


5.966 


72 


44 


24 


64 


I3'ft 


5.667 


44 


40 


56 


86 


35 


5.917 


40 


44 


48 


72 


12 ft 


5.967 


86 


44 


24 


64 


35ft 


5.868 


44 


40 


56 


861 35 


5.918 


64 


40 


28 


72 


16 


5.968 


86 


44 


24 


64 


35ft 


5.869 


44 


48 


56 


86 10 ft 


5.919 


d6 


40 


28 


64 


51 


5.969 


56 


40 


32 


64 


31ft 


5.870 


72 


46 


32 


64 IZVl 


5.920 


40 


48 


56 


72 


24 


5.970 


44 


40 


48 


72 


35ft 


5.871 


86 


40 


24 


72 


35 


5.921 


64 


44 


26 


56 


35ft 


5.971 


44 


40 


48 


86 


13ft 


5.872 


86 


48 


24 


72 


lOfe 


5.922 


86 


64 


40 


72 


37ft 


5.972 


72 


48 


28 


64 


24ft 


5.873 


56 


40 


28 


64 


16ft 


5.923 


66 


64 


40 


72 


37ft 


5.973 


56 


64 


40 


48 


35 


5.874 


40 


48 


56 


72 


25 


5.924 


46 


44 


56 


66 33ft 


5.974 


66 


44 


24 


72 


23«ft 


5.875 


56 


40 


44 


100 


\VA 


5.925 


86 


64 


32 


56 39ft 


5.975 


56 


44 


48 


100 


12 


5.876 


40 


48 


64 


72 


37ft 


5.926 


86 


64 


32 


56 


39 ft 


5.976 


56 


44 


48 


100 


12 


5.877 86 


46 


28 


72 


32 ft 


5.927 


56 


44 


46 


100 


14 


5.977 


86 


40 


24 


72 


33 ft 


5.878 


44 


48 


56 


86 


10 


5.928 


40 


44 


48 


72 


12 


5.978 


64 


44 


24 


56 


16 ft 


5.879 


48 


56 


64 


72 


39 ft 


5.929 


40 


44 


46 


72 


12 


5.979 


72 


44 


24 


56 


31ft 


5.880 86 


56 


32 


72 


30 ft 


5.930 


86 


44 


24 


64 


36 


5.960 


44 


48 


56 


72 


33 


5.881 


86 


46 


24 


72 


10 


5.931 


44 


40 


48 


66 


15 


5.981 


56 


32 


28 


72 


28ft 


5.882 


86 


64 


40 


72 


38 


5.932 


72 


40 


24 


64 


26ft 


5.982 


44 


40 


46 


86 


13 


5.863 


86 


64 


40 


72 


38 


5.933 


44 


40 


48 


72 


36 


5.983 


44 


40 


48 


86 


13 


5.884 


64 


44 


28 


56 


36 


5.934 


64 


40 


26 


72 


17ft 


5.984 


72 


44 


28 


56 


43 


5.885 


72 


44 


28 


56 


44 


5.935 


72 


44 


26 


64 34 


5.985 


40 


56 


64 


72 


19ft 


5.886 


64 


56 


28 


48 


28 


5.936 


56 


40 


32 


64 


32 


5.986 


44 


56 


64 


72 


31 


5.887 


56 


44 


48 


100 


15ft 


5.937 


56 


64 


40 


48 


35ft 


5.987 


44 


56 


64 


72 


31 


5.886 56 


40 


26 


64 


16 


5.938 


44 


40 


56 


86 


34 


5.988 


56 


40 


48 


100 


27 


5.889 


48 


44 


56 


86 


34 


5.939 


40 


44 


48 


72 


life 


5.989 


86 


44 


28 


72 


36 


5.890 


44 


56 


64 


72 


32 ft 


5.940 


86 


56 


32 


72 


29 ft 


5.990 


72 


48 


32 


64 


37 


5.891 


56 


40 


44 


100 


17 


5.941 


86 


48 


26 


72 


31/2 


5.991 


48 


44 


56 


86 


32ft 


5.692 


86 


44 


24 


64 


36'/* 


5.942 


86 


40 


24 


72 


34 


5.992 


40 


48 


64 


72 


36 


5.893 


40 


44 


48 


72 


13'/* 


5.943 


56 


40 


28 


64 


14 


5.993 


40 


48 


64 


72 


36 


5.894 


56 


32 


28 


72 


30 


5.944 


44 


40 


46 


86 


14ft 


5.994 


64 


44 


28 


56 


34ft 


5.695 


44 


40 


48 


72 


36/1 


5.945 


44 


40 


48 


86 


14 ft 


5.995 


44 


46 


64 


86 


28ft 


5.896 


40 


44 


56 


72 


33'/* 


5.946 


44 


48 


56 


72 


33ft 


5.996 


40 


44 


56 


72 


32 


5.897 


40 


44 


56 


72 


33ft 


5.947 


72 


44 


24 


56 


32 


5.997 


64 


40 


32 


72 


32ft 


5.698 


72 


40 


26 


64 


41ft 


5.946 


72 


46 


26 


64 


25 


5.998 


86 


56 


32 


72 


28ft 


15.899 


56 


64 


40 


48 


36 


5.949 


86 


44 


28 


Jl 


36ft 


5.999 


56 


44 


32 


64 


19 ft 



A Treatise on Milling and Milling Machines 415 

Instructions for Using Cam-Milling 
Attachment 




Fig. 313 

For milling face cams the attachment is set as shown in illustration. For cylindrical cams it is set 
at right angles to this position. 



The attachment consists of a head stock E, mounted on the 
slide C, having its ways in the bed plate A, which is bolted to the 
table of the machine. The work spindle is driven through worms 
and wormwheel G by a belt from a separate countershaft running 
on pulley P. There is also provision for applying a crank for hand 
feeding. 

Power feed is recommended because it gives a more even motion 
than can be obtained by hand. The work spindle is left large so 
it can be turned down to suit the master cam and the blanks of the 
cams being milled. 

The attachment is set up as follows: 

Secure the master cam to the work spindle so as to engage the 
roller R, which is located on a bracket fixed to the base plate. The 
slide C is held in working engagement with this roller by the weight 
W. The weight regularly furnished is heavy enough for only the 
lightest work; when heavy milling is to be done, sufficient weight 
must be added. 



416 The Cincinnati Milling Machine Company 

The table of the machine must be adjusted vertically to bring 
the center of the roller on the same horizontal plane with the center 
of the cutter. 

The cam being milled is mounted on the work spindle as shown. 
As the spindle revolves, it follows that a revolving motion is imparted 
to the cam being milled, and in combination with this revolving 
motion there is also a lateral movement caused by the master cam 
rolling against the roller R, which is fixed to the base A. If the 
master cam is properly constructed the resulting cam will be satis- 
factory. 

When cams are cut out of solid stock, a roughing cut should be 
taken first, leaving a small amount for finishing. 

The finishing cutter must always be the same diameter 
as the roller with which the finished cam shall work. 

The Master Cam. In case it is found preferable to use for 
the master cam a cam which is exactly like and the same size as the 
cam to be made, the roller R must be the same diameter as the 
finishing cutter. 

In general, the master cam should be larger than the cam being 
milled, and the roller R should be as large in diameter as possible. 

In laying out such a master cam, decide upon a size for the roller 
R (which may be any convenient size), and then LAY OUT the 

MASTER CAM, CONSIDERING IT AS A CAM WHICH, WHEN OPERATING 
IN CONNECTION WITH THIS ROLLER, WILL HAVE THE SAME THROW 

and the same time AS the cam being made. 

These instructions hold for both face and cylindrical cams. 



A Treatise on Milling and Milling Machines 417 



CHAPTER XXI 

NATURAL TRIGONOMETRIC FUNCTIONS 

Giving the Values of Sines, Cosines, Tangents, Cotangents, 
Secants and Cosecants for all Degrees and Minutes from 

Degrees to 90 Degrees 

These functions are arranged in 45 tables, each of which contains 
the values of these six functions for one angle and its complement. 
This, we believe, makes very much simpler and more useful tables 
than those arrangements which place in separate tables, Sines and 
Cosines, Tangents and Cotangents, Secants and Cosecants. 

For Angles Less than 45°. For all angles up to 45°, the readings 
are made direct from the table. The angle is given at the top left- 
hand corner of the table and the minutes are under the left-hand 
column headed M. Suppose we want to know the value of the 
Sine of an angle of 36°12'. We turn to the table which has the 
angle 36° at its top as on page 430, and then we follow down the 
column headed Sine to the figure opposite 12 (in the left-hand 
column under M), and we find the value .59060. This is the 
Sine of 36°12'. The Cosine, Tangent, Cotangent, Secant and Cose- 
cant are found in exactly the same way. In fact, if these several 
functions are wanted at the same time they may be read from the 
table when we are reading the Sine of the angle. 

For Angles Greater than 45°. We now reverse the above 
process. The names of the functions are given at the bottom of the 
table. The angle is at the bottom right-hand corner and minutes 
are given in the right-hand column over M. We must always 
read UP. Suppose we want to know the value of the Sine of an 
angle of 54°2F. Turning to that table which has the angle 54° 
at the bottom, as on page 429, we find our function over the Sine 
as given at the bottom of the table. We read up in the column 
over M at the right-hand side of the page until we come to 21, 
then read across to the left and in the column over Sine we find 
the value .81259. This is the Sine of 54°21'. The value of the 
Cosine, Tangent, Cotangent, Secant and Cosecant are found in 
exactly the same way. 



418 



The Cincinnati Milling Machine Company 



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A Treatise on Milling and Milling Machines 433 



Table of Decimal Equivalents in inches of Millimeters and 

Fractions of Millimeters 



in in. 


Inches 


mm. 


Inches 


mm. 


Inches 


i _ 

5 o — 


. 00079 


5 11 


= 


. 02047 


2 


= 


. 07874 


;<~o = 


.00157 


2T 

5 ii 


= 


.02126 


3 


= 


.11811 


3 

oil — 


. 00236 


28 

OH 


= 


.02205 


4 


= 


. 15748 


4 _ 

3o — 


.00315 


.-> 


= 


.02283 


5 


= 


. 19685 


3°0 = 


. 00394 


3 

g ti 


= 


.02362 


6 


= 


. 23622 


6 
30 — 


.00472 


3 1 

5 


= 


.02441 


7 


- 


. 27559 


z'o = 


. 00551 


3 2 

5 n 


= 


.02520 


8 


= 


. 31496 


8 

50 ~~ 


.00630 


3 3 

50 


= 


.02598 


9 


= 


. 35433 


9 _ 

5 — 


. 00709 


34 
5 


= 


.02677 


10 


= 


.39370 


10 _ 
3T> — 


.00787 


35 

5 


= 


.02756 


11 


= 


.43307 


1 1 . 
30 


. 00866 


36 

50 


= 


.02835 


12 


= 


.47244 


12 _ 
5 — 


.00945 


3 7 
5 


= 


.02913 


13 


= 


.51181 


1 3 _ 

50 — 


. 01024 


38 

5 


= 


.02992 


14 


= 


.55118 


14 . 
50 — 


.01102 


3 9 
50 


= 


.03071 


15 


= 


. 59055 


15 __ 
30 — 


.01181 


40 
5 


= 


.03150 


16 


= 


. 62992 


16 - 
5 0" — 


.01260 


41 

5 


= 


.03228 


17 


= 


. 66929 


17 . 
50 ~~ 


. 01339 


42 

5 


= 


.03307 


18 


= 


.70866 


1 8 . 

3 — 


.01417 


43 

5 


= 


.03386 


19 


= 


. 74803 


19 _ 
30 — 


.01496 


44 

50 


= 


.03465 


20 


= 


.78740 


20 _ 
30 — 


.01575 


45 

5 


= 


.03543 


21 


= 


.82677 


2 1 _ 
50" — 


.01654 


46 
5 


= 


.03622 


22 


= 


.86614 


22 _ 
30 — 


.01732 


4 7 

5 


= 


.03701 


23 


= 


.90551 


2 3 . 

50 — 


.01811 


4 8 

5 


= 


.03780 


24 


= 


.94488 


24 _ 

a — 


.01890 


4 9 

5 


= 


.03858 


25 


= 


.98425 


2 ft 

30" — 


. 01969 


1 


= 


. 03937 


26 


= 1 


.02362 



10 mm. = 1 Centimeter = 0.3937 inches. 
10 cm. = 1 Decimeter = 3.937 inches. 
10 dm. = 1 Meter = 39.37 inches. 

25.4 mm. = 1 English inch. 



434 



The Cincinnati Milling Machine Company 



Table of Decimal Equivalents of Fractions of an Inch 



8ths. 



32ds. 



64ths. 



64ths. 



Vs = -125 

U = .250 

Y% = .375 

y 2 = -500 

% = .625 

% = .750 

Vs = -875 

16ths. 



1 

16 


= 


.0625 


3 
16 


= 


.1875 


5 

16 


= 


.3125 


7 
16 


= 


.4375 


9 
16 


= 


.5625 


11 
16 


= 


.6875 


13 
16 


= 


.8125 


15 

16 


= 


. 9375 



3 
32 



5 _ 
32 — 



7 

32 — 



9 

32 



11 
32 



13 
32 



15 

32 — 



17 

32 — 



19 _ 

32 — 



21 
32 



23 _ 
32 — 



25 _ 
32 — 



27 
32 



29 _ 
32 — 



31 

32 — 



.03125 

.09375 

. 15625 

.21875 

.28125 

34375 

40625 

46875 

, 53125 

59375 

65625 

71875 

78125 

84375 

90625 

96875 



i 

64 



7 
64 



9 
64 



11 
64 



13 
64 



15 
64 



17 
64 



19 
64 



21 
64 



23 
64 



25 
64 



27 
64 



29 
64 



31 
64 



. 015625 
, 046875 
.078125 
. 109375 
. 140625 
, 171875 
, 203125 
234375 
265625 
296875 
328125 
359375 
390625 
421875 
453125 
484375 



33 _ 
64 — 



35 _ 
64 — 



37 

64 — 



39 
64 



41 _ 
64 — 



43 _ 
64 — 



45 _ 
64 — 



47 _ 
64 — 



49 _ 
64 — 



51 _ 
64 — 



53 _ 
64 — 



55 
64 



57 
64 



59 
64 



61 
64 



63 
64 



.515625 
.546875 
.578125 
.609375 
. 640625 
. 671875 
.703125 
. 734375 
.765625 
. 796875 
.828125 
. 859375 
.890625 
.921875 
.953125 
.984375 



Index 



435 



INDEX 



Accuracy of Dividing Heads, 92 
Adapters for Flanging Threaded Spin- 
dle Ends, 112 
Adjustment, Care and Erection of 
Milling Machines, 74 
Adjusting the Spindle, 77 
Care of the Machine, 77 
Countershaft, 74 
Erection, 74 

High Power Machines, 20, 35 
Oiling, 75 

Ordering Repairs, 78 
Removing the Spindle, 76 
Speed of Countershaft, How to 
compute, 75 
Addendum, 281 
Angles and Leads for Spirals, Table 

of, 370 
Angles, Leads and Change Gears for 

Cutting Spiral End Mills, 201 
Angles, Leads and Change Gears for 
Cutting Spiral Milling Cutters, 
201 
Angles, Leads and Change Gears for 

Cutting Twist Drills, 369 
Angular Indexing, 351 
Angular Indexing, Table for, 361 
Arbors, 113 

Arbors, Carried in Stock, 116 
Arbor Equipment for Millers, 115 
Arbors, Key ways for, 113-114 
Arbors, Method of Driving, 111 
Arbors, Proper Arrangement of Sup- 
ports and Cutters on, 109 
Arbor Supports, 108 
Attachments, Milling Machine, 49 
Cam Milling Attachments, 59 
Circular Milling Attachments, 56, 58 
Dividing Heads, 87 
Driving Mechanism, 52 
High Speed Attachment, 53 
Index Heads, Combination, 50 
Indexing Attachments, High Num- 
ber, 51, 97 
Index Basis, 59 
Oil Pumps, 60 



Rack Indexing Attachments, 55 
Rack Indexing Attachment, Table 

for, 298 
Rack Milling Attachments, 55 
Slotting Attachments, 56 
Undercutting Attachments, 52 
Universal Spiral Milling Attach- 
ments, 53 
Vertical Milling Attachments, 54 
Vises, All Steel, 62, 240 
Vises, Plain, Swivel and Tool- 
maker's, 61 
Automatic Clamping and Releasing 

Fixtures, 226-262 
Automatic Indexing Fixtures, 269 
Automatic Millers, 65 
Automatic Releasing Fixtures, 261 



B 



Bevel Gears, Computations for, 305 
Computing the off-set, 316 
Cutting Bevel Gears on a Miller, 310 
Formulas for Bevel Gear Calcu- 
lations, 319 
Outside Diameter of Blank, 309 
Selecting the Cutter, 309 
Setting the Machine, 314 
The Shape of the Tooth, 310 
Tooth Elements, 312 



Cam Milling Attachment, 59-415 
Cams, Spiral Milling, 377 
Care, Erection and Adjustment of 
Milling Machines (see Adjust- 
ment), 74 
Change Gears, for Cutting Spirals, 364 
Application of Continued Fractions 

to, 366 
Change Gear Ratio, 364 
Leads, Change Gears and Angles, 

343 
Leads, Change Gears and Angles 
for Cutting Spiral End Mills, 
201 



436 



Index 



Leads, Change Gears and Angles 
for Cutting Spiral Milling Cut- 
ters, 201 
Leads, Change Gears and Angles 

for Cutting Twist Drills, 369 
Leads, Table of, 372 
Placing Change Gears on the Ma- 
chine, 368 
Chattering, Causes of, 118 
Chattering, Remedies for, 120 
Chip, Influence of Size of, on Life of 

Cutter, 155 
Chips from High Speed Milling, 165 
Chordal Pitch, 280 
Circular Milling Attachment, 56-58 
Circular Pitch, 280 
Clamping Devices for Fixtures, 242 to 

246 
Classification of Milling Machines, 7 
Clearance for Cutters, 207 
Continued Fractions, 351 

Angular Indexing Tables, 361 
Application to Angular Indexing, 

351 
Application to Computing Change 
Gears for Cutting Spirals, 358- 
366 
Application to Gearing a Lathe for 

Metric Threads, 357 
Greatest Common Divisor, 352 
Continuous Milling, 223 and 258 
Coolant, Use of, on Cutters (see Stream 

Lubrication), 156 
Cosecants, Table of, 417 
Cosines, Table of, 417 
Cotangents, Table of, 417 
Cut, Relation of Size of, and Feed to 

Efficiency, 183 
Cutter and Work Cooling System (see 

Stream Lubrication), 156 
Cutter Arbors, 115-116 
Cutter Sharpening, 203 
Cutters, Milling, 171 
Action of, 123 
Capacity of, When Milling Cast 

Iron, 215 
Capacity of, When Milling Steel, 

214 
For Cutting Gears, Table of, 284 
Effect of too many Teeth, 173 
End Mills, Design of, 183 
Face Mills, Cutting Tests on, 182 
Face Mills, Design of, 187 
Form Cutters, Design of, 193 
Helical Mills, Design and Use of, 193 
Influence of Size of Chip on Life of, 

155 
Key ways for, 112 
Life of, When Milling Cast Iron, 

155 
Method of Driving Face Mills, 111 



Nicked Teeth, 174 

Proper Arrangement on Arbors, 

109-110 
Proper Clearance, 207 
Rake or Under-Cut Teeth, Influ- 
ence of, 178 
Relation of Size of Cut and Feed to 

Efficiency, 183 
Renewing Worm, 207 
Resetting Work to, 101 
Setting of Machine for Making, 198 
Shell End Mills, Design of, 186 
Side Mills, Design of, 185 
Solid Mills, Their Construction, 171 
Speeds of (see under Speeds), 207 
Spiral Mills, Correct Design of, 174 
Splining Cutters, Saws, Slotting 

Cutters, etc., Design of, 191 
Table of Leads, Angles, etc., for 

making End Mills, 201 
Table of Leads, Angles, etc., for 

Making Spiral Mills, 201 
Tests on Face Mills, 182 
Tests on Spiral Milling Cutters, 

177 
Twenty-Five Degree Spiral Angle, 

Action of, 175 
Wide-Spaced Teeth, Influence of, 
207 
Cutting Bevel Gears on the Miller, 310 
Cutting Capacity of a Miller, 214 
Cutting Speeds, Experiments on, 158 
Cutting Speeds, Safe Practical, 141 

and 151 
Cutting Spiral Gears on the Miller, 325 
Cutting Spur Gears on the Miller, 285 
Cutting Worm Gears on the Miller, 
347 



D 



Decimal Equivalents of Fractions of 
an Inch, Table of, 434 

Decimal Equivalents of Millimeters, 
Table of, 433 

Dedendum, 281 

Diametral Pitch, 280 

Dividing Head, Accuracy of, 92 

Dividing Head, Care of, 95 

Dividing Head, How to Set Up for 
Indexing a Gear, 97 

Dividing Heads, Causes and Remedy 
for Inaccurate Indexing, 96 

Dividing Heads, Universal, 87 

Divisor, Greatest Common, 352 

Drives for Arbors, 111 

Drives, Motor, 30, 46 

Driving Mechanism for Spiral Cut- 
ting, 52 



Index 



437 



E 

Efficiency, Relation of Size of Cut and 

Feed to, 183 
End Mills, Design of, 183 
End Mills, Feeds and Speeds, Curves 

for, 147 
End Mills, Sharpening, 208 
Equivalents, Decimal, of Fractions of 

an Inch, 434 
Equivalents, Decimal, of Millimeters, 

433 
Erection, Care and Adjustment of 

Milling Machines (see Adjust- 
ment), 74 
Estimating Milling Work (see Power 

Required to do Milling), 213 



F 



Face Milling in Cast Iron, 147 

Face Milling in Steel, 148 

Face Mills, Action of, 128 

Face Mills, Correct Tooth Outline, 121 

Face Mills, Cutting Tests on, 182 

Face Mills, Design of, 187 

Face Mills, Flanged Spindle End for 

Driving, 111 
Face Mills, Influence of Diameter of, 

on Production, 223 
Face Mills, Sharpening, 209 
Feed, Relation of Size of Cut and 

Feed to Efficiency, 183 
Feeds and Speeds of Cutters (see 

Speeds of Milling Cutters), 135 
Feeds, Influence on Production, 133 
Feeds, Milling Machine, 132 

In Thousandths per Revolution, 133 
In Inches per Minute, 133 
Intermittent, 42-43, 66 
Roughing and Finishing Cuts, 103 
Two Systems in Use, 132 
Finishing Cuts in Cast Iron, 144 
Finishing Cuts in Steel, 147 
Fixtures, Automatic Clamping and 

Releasing, 226-262 
Fixtures, Milling Jigs and, 229 

Accessibility for Inserting and Re- 
moving Work, 235 
Automatic Clamping, Releasing and 

Ejecting Fixtures, 262 
Automatic Indexing Fixtures, 269 
Automatic Releasing Fixtures, 261 
Axioms for the Fixture Designer, 

233 
Clamps, 242 to 247 
Elimination of Clamping Strains 

from Table of Machine, 236 
Generous Ducts for Escape of 

Chips and Lubricant, 235 
Hand Indexing Fixtures, 264 to 269 



Loading Fixtures, 254 

Maintenance Cost, 231 

Provision in Excess of Needed 

Rigidity, 237 
Rapidity of Clamping, 235 
Reciprocal Fixtures, 159 
Removal of Clamping Members 

from Cutter Zone, 236 
Right Angle or Square Fixture, 256 
Rotary, Continuous Milling Fix- 
tures, 258 
Rotary, Square or Reciprocating, 

229 
Separation of Swiveling and Index- 
ing Functions, 275 
Setting Pieces, 247 
Simple Fixture for One Piece, 249 
Skill of Workman as a Factor in 

Fixture Design, 231 
Standard Parts of Fixtures, 241 
Support Pins, 241 
Swiveling Fixtures, 271 
Tandem Fixtures, String Jigs, 250 
Vises Used as Fixtures, 238 
Flanged Spindle End, 111 
Flanges for Threaded Spindle Ends, 

112 
Formulas for Bevel Gear Calcula- 
tions, 319 
Formulas for Computing Change 

Gears, 358, 365 
Formulas for Indexing, 99 
Formulas for Mitre Gears, 319 
Formulas for Spiral Gears, 325 to 341 
Formulas for Spur Gears, 289 
Formulas for Worm Gears, 344 
Fractions, Continued, 352 



G 



Gashing Angle for Worm Wheels, 

Table of, 350 
Gashing Worm Wheels (Cutting), 347 
Gear Cutters, Sharpening, 210 
Gear Cutters, Standard Involute, 

Table of, 284 
Gear Teeth, Metric System, 292 
Gear Teeth, Module System, 292 
Gears, Bevel, Rules and Formulas 
for, 319 
Bevel Gears, Cutting, on the Mil- 
ler, 310 
Bevel Gears, Sizing and Cutting (see 
Bevel Gears), 305 
Gears, Mitre, Rules and Formulas 
for, 319 
Mitre Gears, Cutting, on the Miller, 

310 
Mitre Gears, Sizing and Cutting 
(see Bevel Gears), 305 



438 



Index 



Gears, Spiral, Rules and Formulas 
for, 325 to 341 
Spiral Gears, Cutting, on the Mil- 
ler, 325 to 341 
Spiral Gears, Sizing and Cutting 
(see Spiral Gears), 323 
Gears, Spur, Rules and Formulas for, 
289 
Spur Gears, Cutting, on the Miller, 

285 
Spur Gears, Sizing and Cutting (see 
Spur Gears), 279 
Gears, Worm, Rules and Formulas 
for, 344 
Worm Gears, Cutting, on the Mil- 
ler, 347 
Worm Gears, Gashing, 347 
Worm Gears, Hobbing, 349 
Worm Gears, Sizing and Cutting 
(see Worm Gears), 342 
Grinding Milling Cutters Properly 
(see Cutter Sharpening), 207 



H 



Heads, Combination, 50 

Heads, Gear Cutting, 50 

Heads, Plain, 50 

Heads, Spiral, 50 

Heads, Universal Indexing and Divid- 
ing, 87 

Heat, Generation of, by Cutting 
Tools, 156 

Helical Mills, Cutting Tests on, 178 
to 181 

Helical Mills, Design of, 193 

High Number Indexing Attachment, 
51 and 97 

High Speed Milling Attachment, 53 

Hobbing Worm Wheels, 349 



Index Heads, Plain, 50 

Index Heads, Universal, 87 

Indexing, Angular, 351 

Indexing Attachment, High Number, 

51 and 97 
Indexing, Causes of and Remedies for 

Inaccuracies, 96 
Indexing Fixtures, Automatic, 269 
Indexing Fixtures, Hand, 264 
Indexing, How to Calculate, 97 
Indexing, How to Set up for, 97 
Indexing, Methods Employed, 98 
Indexing, Tables, 103 
Index Plates, Uses of Notches in, 101 
Index Bases, 59, 227 
Intermittent Feed, 42, 43, 46 



Jig, String, 219 



K 



Keyway Milling, Speeds and Feeds 

for, 149 
Keyways, for Cutters and Arbors, 

113 and 114 



Lead of a Spiral Gear, How to Com- 
pute, 331 

Leads, Angles and Change Gears for 
Spirals, Table of, 370, 371 

Leads, Change Gears and Angles for 
Cutting Twist Drills, 369 

Leads, Change Gears and Angles for 
Making Spiral Mills, 201 

Leads, Change Gears and Angles for 
Making Spiral End Mills, 201 

Leads, Table of, 372 

Life of Cutters Milling Cast Iron, 153 

Lubrication of Cutters (see Stream 
Lubrication), 156 



M 

Maintenance Cost of Fixtures, 231 
Manufacturing Millers, 71, 72, 
Metric Pitches, 292 
Millimeters, Decimal Equivalents of, 

in Inches, 433 
Milling, An Analysis of the Process of, 
122 
Automatic Clamping and Releasing 

Fixtures, 226 
Continuous Milling, 223 and 258 
Horizontal Machine, Using a String 

Jig, 219 
Horizontal Machine, Using One 

Vise, 218 
Horizontal Machine, Using Two 

Vises, 219 
Influence of Diameter of Face Mill, 

223 
Power Required to Do, 213 
Relation Between Face Milling and 

Spiral Milling, 221 
Revolution Marks, 126 
The Action of a Face Mill, 128 
The Action of a Side Mill, 130 
The Action of a Spiral Mill, 123 
Tooth Marks, 126 
Various Methods of, 217 
Vertical Milling with One Vise, 220 
Vertical Milling with Two Vises, 221 
Milling, Continuous, 223 and 258 



Index 



439 



Milling Cutters, Life of, When Mill- 
ing Cast Iron, 153 
Milling Cutters, Speeds of, 135 
Milling Machines: 

Attachments, 49 

Automatic, 65 

Erection, Care and Adjustment of, 
74 

High Power, Nos. 2 and 3, 20 

High Power, Nos. 4 and 5, 35 

Manufacturing, 7, 72 

M-Type, 11 

Names of Parts 79 to 84 

Plain, 9 

Setting Up, 108 

Selection of, 8 

Universal, 86 

Vertical, 18, 32 and 47 
Milling Machines, Classification of, 7 
Mitre Gears (see Bevel Gears), 305 
Module Pitches, 292 
Motor Drives, 30, 46 



N 



Names of Parts of Milling Machines, 

79 to 84 
Notched Index Plate, Uses of, 102 



O 



Oiling, 75 

Oil Pumps (see also Stream Lubri- 
cation), 60 
Ordering Repairs, Instructions for, 78 



Parts of Milling Machines and Their 

Names, 79 to 84 
Pitch, Chordal, 280 
Pitch, Circular, 280 and 282 
Pitch, Diameter, Spur Gears, 281 
Pitch, Diametral, 280 
Pitch, Metric, 292 
Pitch, Module, 292 

Pitches, Comparative Table of Cir- 
cular and Diametral, 292 
Plain Milling Machines, 7-9 
Plate, Index, Use of Notches in, 102 
Power Required to do Milling, 213 
Capacity of Cutters for Milling 

Cast Iron, 215 
Cutting Capacity of a Machine in 

Cubic Inches, 214 
How to Compute the Power of a 
Cone-Driven Machine, 213 



How to Compute the Power of a 
High-Power Single Pulley Ma- 
chine, 214 
Other Factors Governing Produc- 
tion, 215 
Practical Cutting Speeds, Safe, 141 

and 151 
Pressure Angles of Gear Teeth, 283 
Process of Milling, an Analysis of 

the, 122 
Production, Influence of Speed on, 138 
Proportion, Trigonometry Expressed 

as, 302 
Pumps, Oil (see also Stream Lubri- 
cation), 60 



R 



Rack Indexing Attachment, 55 
Rack Milling Attachment, 55 
Racks, Tables for Indexing and Cut- 
ting, 294 to 298 
Rake or Undercut Value of, in Cut- 
ters, 178 
Reciprocal Milling Fixtures, 229 and 

259 
Releasing Fixtures, Automatic, 261 
Repairs, Instructions for Ordering, 78 
Resetting Work to the Cutter, 102 
Revolution Marks, 126 
Rotary Continuous Milling Fixtures, 

258 
Roughing Cuts in Cast Iron, 142 
Roughing Cuts in Steel, 147 



Secants, Table of, 417 
Selection of a Miller, 8 
Setting up the Machine, 108 
Sharpening End Mills, 208 
Sharpening Face Mills, 209 
Sharpening Gear Cutters, 210 
Sharpening Hand Reamers, 208 
Sharpening Milling Cutters Properly, 

203 to 207 
Sharpening Spiral Mills, 203 to 206 
Shop Trigonometry, Bevel Gears, 299 
Application to a Shop Problem, 

Bevel Gears, 305 
Definition of Sine, etc., 301 
The Right Angle Triangle, 299 
Trigonometric Tables, How to Use, 

304 
Trigonometry Expressed as Pro- 
portion, 302 



440 



Index 



Side Mill, Action of, 130 
Sines, Table of, 417 
Slotting Attachment, 56 
Speeds of Milling Cutters, 135 

Conditions Determining Proper 

Speed, 137 
End Mills, Curves for, 145 
Face Milling in Cast Iron, Curves 

for, 147 
Face Milling Steel Castings, Curves 

for, 148 
Finishing Cast Iron with Spiral 

Mills, Curves for, 144 
Heating, Causes of, 135 
Influence of Speed on Production, 

138 
Keyway Cutting, Curves for, 149 
Life of Cutter, Influence of Size of 

Chip on, 155 
Life of Cutters when Milling Cast 

Iron, 153 
Other Factors which Determine 

Life of Cutters, 152 
Roughing Cast Iron with Spiral 

Mills, Curves for, 142 
Safe, Practical Speeds for Cutters, 

141 and 151 
Spiral Milling in Cast Iron, Curves 

for, 142 
Spiral Milling in Steel, Curves for, 
147 
Spindle End, Flanged, 111 
Spindle Ends, Flanges for Threaded, 

112 
Spindle, Instructions for Adjusting, 77 
Spindle, Instructions for Removing, 76 
Spiral Cams, 377 

Spiral Cutting, Change Gears for, 364 
Spiral Gear Cutting, 323 

Cutting Spiral Gears on the Mil- 
ler, 325 to 341 
Pitch, Lead, Normal Pitch, etc., 324 
Selecting the Cutter, 327 
Spiral Gears with Shafts at an Angle 
of Less than 90°, 337 
Diameters, Circumferences, etc., 

339 
Number of Teeth and Spiral Angle, 
338 
Spiral Gears with Shafts at Right 
Angles, Computations for, 332 
Computing the Lead, 335 
Number of Teeth and Spiral Angle, 

332 
Selecting the Cutter, 335 
Spiral Gears with Shafts Parallel, 
Computations for, 327 
Computing the Lead, 331 
Number of Teeth and Spiral Angle, 

328 
Selecting the Cutter, 330 



Spiral Mills, Cutting Tests on, 177 to 

182 
Spiral Mills, Sharpening, 203 to 207 
Spiral Mills, Design of, 174 
Spiral Mills, Making, 198 
Spur Gears, Sizing and Cutting, 279 
Addendum and Dedendum, 281 
Center Distance, 281 
Chordal Pitch, 280 
Circular Pitch, 280 and 282 
Clearance and Full Depth, 282 
Cutters for Cutting Gears, Table of 

Standard, 284 
Cutting Gears on the Miller, 285 
Cutting Large Gears, 287 
Diametral Pitch, 280 
Number of Teeth, 281 
Outside Diameter, 282 
Pitch Diameter, 281 
Pitches, Comparative Table of Cir- 
cular and Diametral, 292 
Pressure Angles,. 283 
Racks, Table for Cutting, 294 to 298 
Rules and Formulas for Dimensions 

of Spur Gears, 289 
Selecting the Cutter, 284 
Setting the Machine, 286 
Sharpening Gear Cutters, 210 
Table of Tooth Parts, 288 
Spiral Heads, 50 and 87 
Spiral Milling Attachment, Universal 

53 
Stream Lubrication, Cutter and Work 
Cooling, 156 
Application to Heavy Cuts, 170 
Application to Light Finishing Cuts, 

170 
Chips from High Speed Milling, 165 
Cutter Hoods, 168, 169 
Cutting Speeds, Experiments on, 

158 
Effects of Ample Lubrication at 

High Speeds, 163 
Generation of Heat by Cutting 

Tools, 156 
Kinds of Lubricant, 167 
Standard Equipment, 169 
The Pump, 167 
Swiveling Fixtures, 271 



Tailstock, Dividing Head, 91 

Tandem Fixtures, 250 

Tangents, Table of, 417 

Teeth, Wide Spaced, in Spiral Mills, 

178 
Toolroom Millers, 86 
Tooth Marks, 126 
Tooth Parts of Gears, Table of, 288 
Trigonometric Functions, 416 



Index 



441 



Trigonometric Tables, 417 
Trigonometry Expressed as Propor- 
tion, 302 
Trigonometry, Shop, 299 



U 



Undercut or Rake, Value of, in Cut- 
ters, 178 to 182 
Undercutting Attachment, 52 
Universal Dividing Heads, 87 
Universal Spiral Milling Attachment, 

53 
Universal ToolroomMillers, 86 



Various Methods of Milling, 217 
Vertical Attachments, 54 
Vertical Continuous Milling, 223 
Vertical Milling Machines, 18, 32 and 

47 
Vises, All Steel, 62 



Vises, All Steel, Use of as Fixtures, 

238 to 241 
Vises, Milling Machine, 61 
Vise, Use of One as a Fixture, 218 and 

220 
Vise, Use of Two as a Fixture, 187 and 

221 



W 



Wide Spaced Teeth in Spiral Mills, 178 
Worm Gearing, 342 

Cutting the Worm Wheel, 347 

Gashing Angle for Worm Wheels, 
Table of, 350 

Hobbing the Worm Wheel, 349 

Outside Diameter, 343 

Practical Example, 346 

Rules and Formulas for, 344, 345 

The Gashing Angle, 347 

Worm Cutting Tool, 343 

Worm Thread Parts, Table of Im- 
portant Dimensions, 346 



